Mixed-Integer Linear Programming (MILP) optimization plus sensitivity analysis

Use of a MILP optimization method and R to choose which hubs (and how many) to use as vehicle preparation and distribution centers for an online car sales company

Premise of this project: Speedy Car Sales (SCS) is a fictional online automobile sales company intending to buy and sell used vehicles throughout the contiguous United States. Their operating model is to buy vehicles throughout the US and ship them to one or more preparation centers, prepare the vehicles, and ship them directly to the customer. SCS believes it can make up for the expense of two-way shipping cost by having fewer distribution centers which are models of efficiency. At the distribution centers, the vehicles will be inspected, cleaned, repaired, if necessary, and photographed for online sales. The vehicles will then be shipped to a buyer.

MILP Optimization will be conducted using R and Microsoft Excel.

Step 1: Gather population data

In this fictional model, SCS will buy and sell USED vehicles throughout the US. Well, were are the vehicle coming from and going to? Where the people are! Let’s get US population data by county or city.
There are many databases and methods of showing population and/or population density. With much credit here: https://homepage.divms.uiowa.edu/~luke/classes/STAT4580/maps.html#county-population-data, we can show population data by county.

Display population by county

if (! file.exists("PEP_2018_PEPANNRES.zip")) {
  download.file("http://www.stat.uiowa.edu/~luke/data/PEP_2018_PEPANNRES.zip",
                "PEP_2018_PEPANNRES.zip")
  unzip("PEP_2018_PEPANNRES.zip")
}

pep2018 <- read.csv("PEP_2018_PEPANNRES_with_ann.csv")
pepvars <- names(pep2018)
pep2018 <- read.csv("PEP_2018_PEPANNRES_with_ann.csv", stringsAsFactors = FALSE,
                    head = FALSE, skip = 2)
names(pep2018) <- pepvars

#head(pep2018)
#tail(pep2018)

#Working with the county names can be tricky:
  
#head(filter(pep2018, grepl(", Iowa", GEO.display.label)))

#pep2018[1803,]
#filter(pep2018, GEO.id2 == 19141)
#filter(pep2018, GEO.id2 == 22001)

# For US counties it is safer to work with the FIPS county code, which is the GEO.id2 variable.
# 
# The county.fips data frame in the maps package links the FIPS code to region names used by the map data in the maps package.
library(maps)
#head(county.fips)

# Basic Map Data
# Map data from the map function in package maps consists of the x and y coordinates of polygons and names for the regions.

usa <- map("state", fill = TRUE, plot = FALSE)
#plot(usa$x, usa$y, type = "n")
#polygon(usa$x, usa$y)

#sum(is.na(usa$x))
## [1] 62
#length(usa$names)
## [1] 63
#usa$names

library(ggplot2)
gusa <- map_data("state")
#head(gusa)
##        long      lat group order  region subregion
## 1 -87.46201 30.38968     1     1 alabama      <NA>
## 2 -87.48493 30.37249     1     2 alabama      <NA>
## 3 -87.52503 30.37249     1     3 alabama      <NA>
## 4 -87.53076 30.33239     1     4 alabama      <NA>
## 5 -87.57087 30.32665     1     5 alabama      <NA>
## 6 -87.58806 30.32665     1     6 alabama      <NA>
#head(filter(gusa, region == "virginia"))
##        long      lat group order   region  subregion
## 1 -75.64188 37.96418    53 13482 virginia chesapeake
## 2 -75.61897 37.99856    53 13483 virginia chesapeake
## 3 -75.36114 38.02721    53 13484 virginia chesapeake
## 4 -75.39552 37.99283    53 13485 virginia chesapeake
## 5 -75.41843 37.96991    53 13486 virginia chesapeake
## 6 -75.42989 37.94127    53 13487 virginia chesapeake
p <- ggplot(gusa) + geom_polygon(aes(long, lat, group = group), color = "white")
#p


# Approximate Centroids
# A quick approximation to the centroids (centers of gravity) of the polygons is to compute the center of the bounding rectangle.
# 
# This is easiest to do with the data from map_data.
library(dplyr)
state_centroids <- summarize(group_by(gusa, region),
                             x = mean(range(long)), y = mean(range(lat)))
names(state_centroids)[1] <- "state"
#head(state_centroids)

# Symbol Plots of State Population
# Aggregate the county populations to the state level:
  
state_pops <- mutate(pep2018,
                     state = tolower(sub(".*, ", "", GEO.display.label)),
                     pop = respop72018)
#unique(state_pops$state)

state_pops <- summarize(group_by(state_pops, state),
                        pop = sum(pop, na.rm = TRUE))
# Using tolower matches the case in the state_centroids table.
# 
# An alternative would be to use the state FIPS code and the state.fips table.
# 
# Merge in the centroid locations. Using inner_join drops cases not included in the lower-48 map data.

state_pops <- inner_join(state_pops, state_centroids, "state")

#head(state_pops)


# Choropleth Maps of State Population
# A choropleth map needs to have the information for coloring all the pieces of a region.
# 
# For ggplot this can be done by merging:
  
sp <- select(state_pops, region = state, pop)
gusa_pop <- left_join(gusa, sp, "region")
#head(gusa_pop)
##        long      lat group order  region subregion     pop
## 1 -87.46201 30.38968     1     1 alabama      <NA> 4887871
## 2 -87.48493 30.37249     1     2 alabama      <NA> 4887871
## 3 -87.52503 30.37249     1     3 alabama      <NA> 4887871
## 4 -87.53076 30.33239     1     4 alabama      <NA> 4887871
## 5 -87.57087 30.32665     1     5 alabama      <NA> 4887871
## 6 -87.58806 30.32665     1     6 alabama      <NA> 4887871

#A first attempt:
  
# ggplot(gusa_pop) +
#   geom_polygon(aes(long, lat, group = group, fill = pop)) +
#   coord_map("bonne", parameters=45) +
#   ggthemes::theme_map()

# This image is dominated by the fact that most state populations are small.
# 
# Showing population ranks, or percentile values, can help see the variation a bit better.
spr <- mutate(sp, rpop = rank(pop))
gusa_rpop <- left_join(gusa, spr, "region")
# ggplot(gusa_rpop) +
#   geom_polygon(aes(long, lat, group = group, fill = rpop)) +
#   coord_map("bonne", parameters=45) +
#   ggthemes::theme_map()

# Using quintile bins instead of a continuous scale:
ncls <- 6
spr <- mutate(spr,
              pcls = cut(pop, quantile(pop, seq(0, 1, len = ncls)),
                         include.lowest = TRUE))
gusa_rpop <- left_join(gusa, spr, "region")
# ggplot(gusa_rpop) +
#   geom_polygon(aes(long, lat, group = group, fill = pcls),
#                color = "grey") +
#   coord_map("bonne", parameters=45) +
#   ggthemes::theme_map() +
#   scale_fill_brewer(palette = "Reds")

#A percentile bin map using the map function requires a vector of colors for the regions:
  
usa_states <- sub(":.*", "", usa$names)
usa_pcls <- spr$pcls[match(usa_states, spr$region)]
pal <- RColorBrewer::brewer.pal(nlevels(usa_pcls), "Reds")
#map("state", fill = TRUE, col = pal[usa_pcls], border = "grey")

#This uses the match function to find indices for each polygon’s state in the regions vector.

#Another way to compute the classes for the pieces:
library(tidyr) 
usa_pieces <- data.frame(names = usa$names)
usa_pieces <- separate(usa_pieces, "names", c("region", "subregion"),
                       sep = ":", fill = "right")
usa_pieces <- left_join(usa_pieces, spr, "region")
#map("state", fill = TRUE, col = pal[usa_pieces$pcls], border = "grey")


# Choropleth Maps of County Population
# For a county-level ggplot map, first get the polygon data frame:
library(purrr)
library(tidyr)
library(ggplot2)
gcounty <- map_data("county")
#head(gcounty)

#To attach the FIPS code we first need to clean up the county.fips table a bit:
  
#head(filter(county.fips, grepl(":", polyname)))

#Remove the sub-county regions, remove duplicate rows, and split the polyname variable into region and subregion:
  
fipstab <-
  transmute(county.fips, fips, county = sub(":.*", "", polyname))
fipstab <- unique(fipstab)
fipstab <-
  separate(fipstab, county, c("region", "subregion"), sep = ",")
#head(fipstab)

#Now use left_join to merge the FIPS code into gcounty:
  
gcounty <- left_join(gcounty, fipstab, c("region", "subregion"))
#head(gcounty)


#Pull together the data for the map:
ncls <- 6 
cpop <- select(pep2018,
               fips = GEO.id2,
               pop10 = rescen42010,
               pop18 = respop72018)
cpop <- mutate(cpop, rpop18 = rank(pop18))
cpop <- mutate(cpop,
               pcls18 = cut(pop18, quantile(pop18, seq(0, 1, len = ncls)),
                            include.lowest = TRUE))
#head(cpop)

#Some of the counties in the polygon data base may not appear in the population data:
  
#unique(select(filter(gcounty, ! fips %in% cpop$fips), region, subregion))
##         region subregion
## 1 south dakota   shannon
#unique(select(anti_join(gcounty, cpop, "fips"), region, subregion))
##         region subregion
## 1 south dakota   shannon
#A left_join with cpop will give these NA values.

gcounty_pop <- left_join(gcounty, cpop, "fips")
#unique(select(filter(gcounty_pop, is.na(rpop18)), region, subregion))
##         region subregion
## 1 south dakota   shannon
#County level population plots using the default continuous scale:

# ggplot(gcounty_pop) +
#   geom_polygon(aes(long, lat, group = group, fill = rpop18),
#                color = "grey", size = 0.1) +
#   geom_polygon(aes(long, lat, group = group),
#                fill = NA, data = gusa, color = "lightgrey") +
#   coord_map("bonne", parameters=45) + ggthemes::theme_map()


#A discrete scale with a very different color to highlight the counties with missing information:
ggplot(gcounty_pop) +
  geom_polygon(aes(long, lat, group = group, fill = pcls18),
               color = "grey", size = 0.1) +
  geom_polygon(aes(long, lat, group = group),
               fill = NA, data = gusa, color = "lightgrey") +
  coord_map("bonne", parameters=45) + ggthemes::theme_map() +
  scale_fill_brewer(palette = "Reds", na.value = "white") +
  theme(legend.position="none")

This is a pleasant looking map, but doesn’t help us too much for out purposes. This data was separated in to 5 different levels of population by county. It gives us false impressions of high population areas. For instance, look at Arizona and Texas. Because the counties are so big in Arizona, it looks like the entire state is deep red and has a lot higher population than it actually does whereas Texas looks moderately populated. The same with Wyoming, which gives the appearance of being heavily populated.

Fortunately, the Internet can link us up with U.S. Census data to get estimated population by city and also by metro area.

Display population data by metro area

# us map of states and populations
library(tidyverse)

library(ggplot2)

# "us.cities" in maps package contains This database is of us cities of population
# greater than about 40,000. Also included are state capitals of any 
# population size.
# "state" database produces a map of the states of the United States
# mainland generated from US De- partment of the Census data
library(maps)

us_states <- as_tibble(map_data("state"))
us_cities <- as_tibble(us.cities)

us_cities <-us_cities %>% 
  filter(country.etc != "AK") %>% 
  filter(country.etc != "HI")

ggplot(data = us_states, mapping = aes(x = long, y = lat,
                                       group = group)) +
  geom_polygon(fill= "white", color = "black") +
  geom_point(data = us_cities, aes( x = long, y = lat,
                                    size = pop, color = "purple", alpha = 0.5),
             inherit.aes = FALSE)

To do: put legend at bottom. Maybe use previous map change colors of each size

The plot above gives us a better representation of population centers. Arizona now shows only a few population centers around Phoenix and Tucson. The heavily populated areas of Los Angeles/San Diego, San Francisco/Oakland, Chicago, Boston New York, Washington D.C., Miami, etc… are clearly shown better.

In the above, AK and HI are removed. There are 1,001 cities in this data base with populations greater than 40,000. That is doable for advanced commercial optimization algorithms, but too many for what we want to do and certainly too many for the Solver that comes with MS Excel.

Modeling our business

In our fictional sales company, it is in the early growth stage.

For this stage, we will assume they have just one hub and are looking to expand. The car company started in Houston, TX and that is where their distribution center is.

For this next phase however, we won’t use individual cities. Each new hub costs a lot in new capital. Using cities data might skew our results towards states with very large cities compared to a larger amount of smaller cities pack together in metro areas. If we chose the top 25 or so cities, quite a few California cities might make the cut and might leave out Washington D.C. But U.S. Census data is available for metro areas.

After some data wrangling, we chose the top 45 areas plus a few extras, like Spokane, WA. The first six (out of 50) of our data set looks like this below:

#### import data set ####
library(readr)
library(tidyr)
# Read in .csv file and create Tibble DF.
cities_raw <- read_csv("my_top_50.csv")
head(cities_raw)
## # A tibble: 6 x 4
##   City        State         `City, State`           Population
##   <chr>       <chr>         <chr>                        <dbl>
## 1 Albuquerque New Mexico    Albuquerque, New Mexico     918018
## 2 Atlanta     Georgia       Atlanta, Georgia           6020364
## 3 Baltimore   Maryland      Baltimore, Maryland        2800053
## 4 Birmingham  Alabama       Birmingham, Alabama        1090435
## 5 Boise       Idaho         Boise, Idaho                749202
## 6 Boston      Massachusetts Boston, Massachusetts      4873019

show map with 50 cities

#### now map it ####
library(tidyverse)


# "us.cities" in maps package contains This database is of us cities of population
# greater than about 40,000. Also included are state capitals of any 
# population size.
# "state" database produces a map of the states of the United States
# mainland generated from US De- partment of the Census data
library(maps)
library(ggmap)

# Read in 10 city data with distances made in "Get Distances"
cities_50 <- read_csv("distances_my_top_50.csv")

# Get states for plotting state map
us_states <- as_tibble(map_data("state"))


ggplot(data = us_states, mapping = aes(x = long, y = lat,
                                       group = group)) +
  geom_polygon(fill= "white", color = "black") +
  geom_point(data = cities_50, aes( x = lon.from, y = lat.from,
                                    size = from_population, color = "purple", alpha = 0.5),
             inherit.aes = FALSE) +
  geom_text(data = cities_50, aes(x = lon.from, y = lat.from, label = from), inherit.aes = FALSE) #+

  # geom_segment(data = cities_10, aes(x = lon.from, y = lat.from, xend = lon.to[5],
  #                                       yend = lat.to[5]), color = "blue", size = 0.3,
  #              arrow = arrow(), inherit.aes = FALSE)

Now we have metro area and state. Each metro area has been named by it’s prominent city. For example, the New York metro area consists of New York, NY, Newark, NJ, and the surrounding small cities. It is lableled just “New York”. This will allow us to calculate distances very easily via Google’s API serice which uses Lat/Long or City/State. We are using City/State here.

In our fictional company, they are currently buying and selling 4,000 car per month. Why 4,000? Thanks for asking. The company did $1.6B in sales in 2019. With an average selling price of $30000 per vehicle, that is xxxx a year and xxx a month. Let’s assume they are growing. That is 4,000 cars a month.

We

We want to start with a small problem to make sure we are doing it correctly so will use the 10 largest metro areas.

For this optimization, we have 10 cities and 1 hub. As mentioned earlier, the amount of buying and selling is related to the population. If New York metro is 19,000,000 and Los Angeles metro is 9,500,000, NY will have twice the sales of LA.

For our 50, we filter to the top 10. Then we get the ratio of each city to the 10-city total and multiple by 4,000. Here is our result:

cities_10 <- read_csv("distances_top_10.csv")
cities_10 %>% 
  select(from, to, from_num_cars) %>% 
  filter(to == "Houston, Texas" )
## # A tibble: 10 x 3
##    from                             to             from_num_cars
##    <chr>                            <chr>                  <dbl>
##  1 New York, New York               Houston, Texas           893
##  2 Los Angeles, California          Houston, Texas           614
##  3 Chicago, Illinois                Houston, Texas           440
##  4 Dallas, Texas                    Houston, Texas           352
##  5 Houston, Texas                   Houston, Texas           328
##  6 Washington, District of Columbia Houston, Texas           292
##  7 Miami, Florida                   Houston, Texas           287
##  8 Philadelphia, Pennsylvania       Houston, Texas           284
##  9 Atlanta, Georgia                 Houston, Texas           280
## 10 Phoenix, Arizona                 Houston, Texas           230

show map with 10 cities

#### now map it ####
library(tidyverse)


# "us.cities" in maps package contains This database is of us cities of population
# greater than about 40,000. Also included are state capitals of any 
# population size.
# "state" database produces a map of the states of the United States
# mainland generated from US De- partment of the Census data
library(maps)
library(ggmap)

# Read in 10 city data with distances made in "Get Distances"
cities_10 <- read_csv("distances_top_10.csv")

# Get states for plotting state map
us_states <- as_tibble(map_data("state"))


ggplot(data = us_states, mapping = aes(x = long, y = lat,
                                       group = group)) +
  geom_polygon(fill= "white", color = "black") +
  geom_point(data = cities_10, aes( x = lon.from, y = lat.from,
                                    size = from_population, color = "purple", alpha = 0.5),
             inherit.aes = FALSE) +
  geom_text(data = cities_10, aes(x = lon.from, y = lat.from, label = from), inherit.aes = FALSE) #+

  # geom_segment(data = cities_10, aes(x = lon.from, y = lat.from, xend = lon.to[5],
  #                                       yend = lat.to[5]), color = "blue", size = 0.3,
  #              arrow = arrow(), inherit.aes = FALSE)

Get Cost of Shipping

For our optimization, we need something to optimized. We are going to optimize shipping costs. Specifically, we will minimize costs.
We figured that shipping costs might come in two sub-costs. 1) labor to load and unload and 2) cost by mile to ship. Looking through some shipping websites, it is quickly discovered that costs decrease for longer shipping distances. After some trial and error, we came up with the following shipping cost function:
shipping cost (in dollars) = 100 (load and unload labor) + 100 *sqrt(distance)
It looks like this:

m <- matrix(0, ncol = 2, nrow = 4000)
dist <- data.frame(m)
x <- c("Distance", "Cost")
colnames(dist) <- x
dist$Distance <- c(seq(1, 4000))
dist$Cost <- sapply(dist$Distance, function(x) 100 + 15*sqrt(x))
#head(dist)
plot(dist$Distance,dist$Cost)

first look, 10 C, 1H

For optimization,

INSERT Equation

\[\sum_{i=1}^n X_i\]

*** Insert image of Excel

First we need cost of shipping:

Show equation

Show getting distances
show results

Show Excel
Trivial problem - 10 Cities, 1 hub

Do it in R

library(ompr)
library(magrittr)
## 
## Attaching package: 'magrittr'
## The following object is masked from 'package:ggmap':
## 
##     inset
## The following object is masked from 'package:purrr':
## 
##     set_names
## The following object is masked from 'package:tidyr':
## 
##     extract
library(ROI)
## ROI: R Optimization Infrastructure
## Registered solver plugins: nlminb, glpk.
## Default solver: auto.
library(ROI.plugin.glpk)
library(ompr)
library(ompr.roi)
# Shipping Cost
cost <- c(705.04,690.03,593.44,332.01,100.00,662.94,617.15,689.96,522.36,614.42)
# Supply to move from each cities
supply <- c(893,614,440,352,328,292,287,284,280,230)

model <- MIPModel()  %>% 
  # Number of cars shiped from Xi to Xj
  add_variable(x[i], i = 1:10, type = "integer", lb = 0) %>% 
  # minimize shipping cost
  set_objective(sum_expr(cost[i] * x[i], i = 1:10), "min") %>% 
  # must use supply from each city
  add_constraint(x[i] >= supply[i], i = 1:10) #%>% 
## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.
  # use only one Y
  #add_constraint(sum_expr(y[j], j = 1:2) == 1) %>% 
  # add linking variables
  
#result <- ROI_solve(model, solver = "glpk")
# result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
# result
# get_solution(result, x[i])


result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
## <SOLVER MSG>  ----
## GLPK Simplex Optimizer, v4.65
## 10 rows, 10 columns, 10 non-zeros
##       0: obj =   0.000000000e+00 inf =   4.000e+03 (10)
##      10: obj =   2.318286830e+06 inf =   0.000e+00 (0)
## OPTIMAL LP SOLUTION FOUND
## GLPK Integer Optimizer, v4.65
## 10 rows, 10 columns, 10 non-zeros
## 10 integer variables, none of which are binary
## Integer optimization begins...
## Long-step dual simplex will be used
## +    10: mip =     not found yet >=              -inf        (1; 0)
## +    10: >>>>>   2.318286830e+06 >=   2.318286830e+06   0.0% (1; 0)
## +    10: mip =   2.318286830e+06 >=     tree is empty   0.0% (0; 1)
## INTEGER OPTIMAL SOLUTION FOUND
## <!SOLVER MSG> ----
result
## Status: optimal
## Objective value: 2318287
get_solution(result, x[i])
##    variable  i value
## 1         x  1   893
## 2         x  2   614
## 3         x  3   440
## 4         x  4   352
## 5         x  5   328
## 6         x  6   292
## 7         x  7   287
## 8         x  8   284
## 9         x  9   280
## 10        x 10   230
cities_10 <- read_csv("distances_top_10.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
solution <- as_tibble(get_solution(result, x[i]))
solution$FROM_city <- c(cities_10$from[1:10])
solution$TO_city <- "Houston, Texas"
names(solution)[3] <- "# Cars Shipped"
solution
## # A tibble: 10 x 5
##    variable     i `# Cars Shipped` FROM_city          TO_city       
##    <chr>    <int>            <dbl> <chr>              <chr>         
##  1 x            1              893 New York, New York Houston, Texas
##  2 x            2              614 New York, New York Houston, Texas
##  3 x            3              440 New York, New York Houston, Texas
##  4 x            4              352 New York, New York Houston, Texas
##  5 x            5              328 New York, New York Houston, Texas
##  6 x            6              292 New York, New York Houston, Texas
##  7 x            7              287 New York, New York Houston, Texas
##  8 x            8              284 New York, New York Houston, Texas
##  9 x            9              280 New York, New York Houston, Texas
## 10 x           10              230 New York, New York Houston, Texas
library(ggmap)
ggplot(data = us_states, mapping = aes(x = long, y = lat,
                                       group = group)) +
  geom_polygon(fill= "white", color = "black") +
  geom_point(data = cities_10, aes( x = lon.from, y = lat.from,
                                    size = from_population, color = "purple", alpha = 0.5),
             inherit.aes = FALSE) +
  geom_text(data = cities_10, aes(x = lon.from, y = lat.from, label = from), inherit.aes = FALSE) +
  geom_segment(data = cities_10, aes(x = lon.from, y = lat.from, xend = lon.to[5],
                                        yend = lat.to[5]), color = "blue", size = 0.3,
               arrow = arrow(), inherit.aes = FALSE)

10 C 2 H

equation

Show Excel
Trivial problem - 10 Cities, 2 hubs

R solution

library(ompr)
library(magrittr)
library(ROI)
library(ROI.plugin.glpk)
library(ompr)
library(ompr.roi)
# Shipping Cost
cost <- c(705.04,690.03,593.44,332.01,100.00,662.94,617.15,689.96,522.36,614.42,
          326.04,874.85,496.92,646.68,662.94,100.00,586.57,277.47,478.96,819.49)
cost_m <- matrix(cost, nrow = 10, byrow = FALSE)
cost_m
##         [,1]   [,2]
##  [1,] 705.04 326.04
##  [2,] 690.03 874.85
##  [3,] 593.44 496.92
##  [4,] 332.01 646.68
##  [5,] 100.00 662.94
##  [6,] 662.94 100.00
##  [7,] 617.15 586.57
##  [8,] 689.96 277.47
##  [9,] 522.36 478.96
## [10,] 614.42 819.49
# Supply to move from each cities
supply <- c(893,614,440,352,328,292,287,284,280,230)

model <- MIPModel()  %>% 
  # Number of cars shiped from Xi to Xj
  add_variable(x[i,j], i = 1:10, j = 1:2, type = "integer", lb = 0) %>% 
  # minimize shipping cost
  set_objective(sum_expr(cost_m[i,j] * x[i,j], i = 1:10, j = 1:2), "min") %>% 
  # must use supply from each city
  
  
  ### fix this with J's, not 1 and 2
  #add_constraint(x[i, 1] + x[i, 2] >= supply[i], i = 1:10) #%>%
  # FIXED! works with j's
  add_constraint(sum_expr(x[i, j], j = 1:2) >= supply[i], i = 1:10) #%>% 
## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.
# use only one Y
#add_constraint(sum_expr(y[j], j = 1:2) == 1) %>% 
# add linking variables

#result <- ROI_solve(model, solver = "glpk")
result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
## <SOLVER MSG>  ----
## GLPK Simplex Optimizer, v4.65
## 10 rows, 20 columns, 20 non-zeros
##       0: obj =   0.000000000e+00 inf =   4.000e+03 (10)
##      10: obj =   2.318286830e+06 inf =   0.000e+00 (0)
## *    16: obj =   1.634916930e+06 inf =   0.000e+00 (0)
## OPTIMAL LP SOLUTION FOUND
## GLPK Integer Optimizer, v4.65
## 10 rows, 20 columns, 20 non-zeros
## 20 integer variables, none of which are binary
## Integer optimization begins...
## Long-step dual simplex will be used
## +    16: mip =     not found yet >=              -inf        (1; 0)
## +    16: >>>>>   1.634916930e+06 >=   1.634916930e+06   0.0% (1; 0)
## +    16: mip =   1.634916930e+06 >=     tree is empty   0.0% (0; 1)
## INTEGER OPTIMAL SOLUTION FOUND
## <!SOLVER MSG> ----
result
## Status: optimal
## Objective value: 1634917
get_solution(result, x[i,j])
##    variable  i j value
## 1         x  1 1     0
## 2         x  2 1   614
## 3         x  3 1     0
## 4         x  4 1   352
## 5         x  5 1   328
## 6         x  6 1     0
## 7         x  7 1     0
## 8         x  8 1     0
## 9         x  9 1     0
## 10        x 10 1   230
## 11        x  1 2   893
## 12        x  2 2     0
## 13        x  3 2   440
## 14        x  4 2     0
## 15        x  5 2     0
## 16        x  6 2   292
## 17        x  7 2   287
## 18        x  8 2   284
## 19        x  9 2   280
## 20        x 10 2     0
temp_df <- as_tibble(get_solution(result, x[i,j]))
temp_df
## # A tibble: 20 x 4
##    variable     i     j value
##    <chr>    <int> <int> <dbl>
##  1 x            1     1     0
##  2 x            2     1   614
##  3 x            3     1     0
##  4 x            4     1   352
##  5 x            5     1   328
##  6 x            6     1     0
##  7 x            7     1     0
##  8 x            8     1     0
##  9 x            9     1     0
## 10 x           10     1   230
## 11 x            1     2   893
## 12 x            2     2     0
## 13 x            3     2   440
## 14 x            4     2     0
## 15 x            5     2     0
## 16 x            6     2   292
## 17 x            7     2   287
## 18 x            8     2   284
## 19 x            9     2   280
## 20 x           10     2     0
### This works!!


#result <- ROI_solve(model, solver = "glpk")
#result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
#result
#get_solution(result, x[i])
cities_10 <- read_csv("distances_top_10.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
solution <- as_tibble(get_solution(result, x[i,j]))
library(dplyr)
#solution
# Adds after the second column
solution <- solution %>%
  add_column(FROM_city = 0) %>% 
  add_column(TO_city = 0) %>% 
  add_column(lon.to = 0) %>%
  add_column(lat.to = 0) %>%
  add_column(lon.from = 0) %>%
  add_column(lat.from = 0)
from.column <- c(cities_10$to[1:10])
to.column <- c("Houston, Texas", "Washington, District of Columbia")
m <- 1
n <- 0
for (k in 1:2){
  for (l in 1:10){
    solution$FROM_city[m] <- from.column[l]
    solution$lon.from[m] <- cities_10$lon.to[l]
    solution$lat.from[m] <- cities_10$lat.to[l]
    solution$TO_city[m] <- to.column[k]
    solution$lon.to[m] <- cities_10$lon.to[5 + n]
    solution$lat.to[m] <- cities_10$lat.to[5 + n]
    m <- m + 1
  }
  n <- n + 1
}

### This works!!!
# no clean it up
solution <- solution %>% 
  filter(value > 0)
solution
## # A tibble: 10 x 10
##    variable     i     j value FROM_city  TO_city lon.to lat.to lon.from lat.from
##    <chr>    <int> <int> <dbl> <chr>      <chr>    <dbl>  <dbl>    <dbl>    <dbl>
##  1 x            2     1   614 Los Angel… Housto…  -95.4   29.8   -118.      34.1
##  2 x            4     1   352 Dallas, T… Housto…  -95.4   29.8    -96.8     32.8
##  3 x            5     1   328 Houston, … Housto…  -95.4   29.8    -95.4     29.8
##  4 x           10     1   230 Phoenix, … Housto…  -95.4   29.8   -112.      33.4
##  5 x            1     2   893 New York,… Washin…  -77.0   38.9    -74.0     40.7
##  6 x            3     2   440 Chicago, … Washin…  -77.0   38.9    -87.6     41.9
##  7 x            6     2   292 Washingto… Washin…  -77.0   38.9    -77.0     38.9
##  8 x            7     2   287 Miami, Fl… Washin…  -77.0   38.9    -80.2     25.8
##  9 x            8     2   284 Philadelp… Washin…  -77.0   38.9    -75.2     40.0
## 10 x            9     2   280 Atlanta, … Washin…  -77.0   38.9    -84.4     33.7
#### now map it ####
library(tidyverse)


# "us.cities" in maps package contains This database is of us cities of population
# greater than about 40,000. Also included are state capitals of any 
# population size.
# "state" database produces a map of the states of the United States
# mainland generated from US De- partment of the Census data
library(maps)

# Read in 10 city data with distances made in "Get Distances"
cities_10 <- read_csv("distances_top_10.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
# Get states for plotting state map
us_states <- as_tibble(map_data("state"))


ggplot(data = us_states, mapping = aes(x = long, y = lat,
                                       group = group)) +
  geom_polygon(fill= "white", color = "black") +
  geom_point(data = cities_10, aes( x = lon.from, y = lat.from,
                                    size = from_population, color = "purple", alpha = 0.5),
             inherit.aes = FALSE) +
  geom_text(data = cities_10, aes(x = lon.from, y = lat.from, label = from), inherit.aes = FALSE) +
  geom_segment(data = solution, aes(x = lon.from, y = lat.from, xend = lon.to,
                                     yend = lat.to), color = "blue", size = 0.3,
               arrow = arrow(), inherit.aes = FALSE)

10 C 2 H Choose 1 or the other

equation

Show Excel
Trivial problem - 10 Cities, 2 hubs R solution

library(ompr)
library(magrittr)
library(ROI)
library(ROI.plugin.glpk)
library(ompr)
library(ompr.roi)
# Shipping Cost
cost <- c(705.04,690.03,593.44,332.01,100.00,662.94,617.15,689.96,522.36,614.42,
          326.04,874.85,496.92,646.68,662.94,100.00,586.57,277.47,478.96,819.49)
cost_m <- matrix(cost, nrow = 10, byrow = FALSE)
cost_m
##         [,1]   [,2]
##  [1,] 705.04 326.04
##  [2,] 690.03 874.85
##  [3,] 593.44 496.92
##  [4,] 332.01 646.68
##  [5,] 100.00 662.94
##  [6,] 662.94 100.00
##  [7,] 617.15 586.57
##  [8,] 689.96 277.47
##  [9,] 522.36 478.96
## [10,] 614.42 819.49
# Supply to move from each cities
supply <- c(893,614,440,352,328,292,287,284,280,230)

model <- MIPModel()  %>% 
  # Number of cars shiped from Xi to Xj
  add_variable(x[i,j], i = 1:10, j = 1:2, type = "integer", lb = 0) %>% 
  # Choose Houston (Y1) or Washington (Y2)
  add_variable(y[j], j = 1:2, type = "binary") %>% 
  #add_variable(y[j], j = 1:2, type = "integer", lb = 0, ub = 1)
  # minimize shipping cost
  set_objective(sum_expr(cost_m[i,j] * x[i,j], i = 1:10, j = 1:2), "min") %>% 
  # must use supply from each city
 
  ### fix this with J's, not 1 and 2
  #add_constraint(x[i, 1] + x[i, 2] >= supply[i], i = 1:10) #%>%
  # FIXED! works with j's
  add_constraint(sum_expr(x[i, j], j = 1:2) >= supply[i], i = 1:10) %>% 
  # use only one Y
  add_constraint(sum_expr(y[j], j = 1:2) == 1) %>% 
  # add linking variables
  add_constraint(x[i,j] <= 1000*y[j], i = 1:10, j = 1:2)
## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.
  # add_constraint(x[i,1] <= 1000*y[1], i = 1:10) %>% 
  # add_constraint(x[i,2] <= 1000*y[2], i = 1:10)
  # 
  # # Not working
  # add_constraint(x[1,1] <= 1000*y[1]) %>% 
  # add_constraint(x[2,1] <= 1000*y[1]) %>%
  # add_constraint(x[3,1] <= 1000*y[1]) %>%
  # add_constraint(x[4,1] <= 1000*y[1]) %>%
  # add_constraint(x[5,1] <= 1000*y[1]) %>%
  # add_constraint(x[6,1] <= 1000*y[1]) %>%
  # add_constraint(x[7,1] <= 1000*y[1]) %>%
  # add_constraint(x[8,1] <= 1000*y[1]) %>%
  # add_constraint(x[9,1] <= 1000*y[1]) %>%
  # add_constraint(x[10,1] <= 1000*y[1]) %>%
  # add_constraint(x[1,2] <= 1000*y[2]) %>%
  # add_constraint(x[2,2] <= 1000*y[2]) %>%
  # add_constraint(x[3,2] <= 1000*y[2]) %>%
  # add_constraint(x[4,2] <= 1000*y[2]) %>%
  # add_constraint(x[5,2] <= 1000*y[2]) %>%
  # add_constraint(x[6,2] <= 1000*y[2]) %>%
  # add_constraint(x[7,2] <= 1000*y[2]) %>%
  # add_constraint(x[8,2] <= 1000*y[2]) %>%
  # add_constraint(x[9,2] <= 1000*y[2]) %>%
  # add_constraint(x[10,2] <= 1000*y[2]) 

#result <- ROI_solve(model, solver = "glpk")
result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
## <SOLVER MSG>  ----
## GLPK Simplex Optimizer, v4.65
## 31 rows, 22 columns, 62 non-zeros
##       0: obj =   0.000000000e+00 inf =   4.001e+03 (11)
##      12: obj =   2.318286830e+06 inf =   0.000e+00 (0)
## *    22: obj =   1.776194770e+06 inf =   0.000e+00 (0)
## OPTIMAL LP SOLUTION FOUND
## GLPK Integer Optimizer, v4.65
## 31 rows, 22 columns, 62 non-zeros
## 22 integer variables, 2 of which are binary
## Integer optimization begins...
## Long-step dual simplex will be used
## +    22: mip =     not found yet >=              -inf        (1; 0)
## +    25: >>>>>   2.090970670e+06 >=   1.902023410e+06   9.0% (2; 0)
## +    25: mip =   2.090970670e+06 >=     tree is empty   0.0% (0; 3)
## INTEGER OPTIMAL SOLUTION FOUND
## <!SOLVER MSG> ----
result
## Status: optimal
## Objective value: 2090971
get_solution(result, x[i,j])
##    variable  i j value
## 1         x  1 1     0
## 2         x  2 1     0
## 3         x  3 1     0
## 4         x  4 1     0
## 5         x  5 1     0
## 6         x  6 1     0
## 7         x  7 1     0
## 8         x  8 1     0
## 9         x  9 1     0
## 10        x 10 1     0
## 11        x  1 2   893
## 12        x  2 2   614
## 13        x  3 2   440
## 14        x  4 2   352
## 15        x  5 2   328
## 16        x  6 2   292
## 17        x  7 2   287
## 18        x  8 2   284
## 19        x  9 2   280
## 20        x 10 2   230
get_solution(result, y[j])
##   variable j value
## 1        y 1     0
## 2        y 2     1
cities_10 <- read_csv("distances_top_10.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
solution <- as_tibble(get_solution(result, x[i,j]))
solution
## # A tibble: 20 x 4
##    variable     i     j value
##    <chr>    <int> <int> <dbl>
##  1 x            1     1     0
##  2 x            2     1     0
##  3 x            3     1     0
##  4 x            4     1     0
##  5 x            5     1     0
##  6 x            6     1     0
##  7 x            7     1     0
##  8 x            8     1     0
##  9 x            9     1     0
## 10 x           10     1     0
## 11 x            1     2   893
## 12 x            2     2   614
## 13 x            3     2   440
## 14 x            4     2   352
## 15 x            5     2   328
## 16 x            6     2   292
## 17 x            7     2   287
## 18 x            8     2   284
## 19 x            9     2   280
## 20 x           10     2   230
library(dplyr)
# get hub solution
solution_hub <- as_tibble(get_solution(result, y[j]))
to.column <- c("Houston, Texas", "Washington, District of Columbia")
solution_hub <- solution_hub %>% 
  add_column(Hub = 0)
solution_hub$Hub <- to.column
solution_hub
## # A tibble: 2 x 4
##   variable     j value Hub                             
##   <chr>    <int> <dbl> <chr>                           
## 1 y            1     0 Houston, Texas                  
## 2 y            2     1 Washington, District of Columbia
# Adds after the second column
solution <- solution %>%
  add_column(FROM_city = 0) %>% 
  add_column(TO_city = 0) %>% 
  add_column(lon.to = 0) %>%
  add_column(lat.to = 0) %>%
  add_column(lon.from = 0) %>%
  add_column(lat.from = 0)
from.column <- c(cities_10$to[1:10])
to.column <- c("Houston, Texas", "Washington, District of Columbia")
m <- 1
n <- 0
for (k in 1:2){
  for (l in 1:10){
    solution$FROM_city[m] <- from.column[l]
    solution$lon.from[m] <- cities_10$lon.to[l]
    solution$lat.from[m] <- cities_10$lat.to[l]
    solution$TO_city[m] <- to.column[k]
    solution$lon.to[m] <- cities_10$lon.to[5 + n]
    solution$lat.to[m] <- cities_10$lat.to[5 + n]
    m <- m + 1
  }
  n <- n + 1
}

### This works!!!
# no clean it up
solution <- solution %>% 
  filter(value > 0)



#### now map it ####
library(tidyverse)


# "us.cities" in maps package contains This database is of us cities of population
# greater than about 40,000. Also included are state capitals of any 
# population size.
# "state" database produces a map of the states of the United States
# mainland generated from US De- partment of the Census data
library(maps)

# Read in 10 city data with distances made in "Get Distances"
cities_10 <- read_csv("distances_top_10.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
# Get states for plotting state map
us_states <- as_tibble(map_data("state"))


ggplot(data = us_states, mapping = aes(x = long, y = lat,
                                       group = group)) +
  geom_polygon(fill= "white", color = "black") +
  geom_point(data = cities_10, aes( x = lon.from, y = lat.from,
                                    size = from_population, color = "purple", alpha = 0.5),
             inherit.aes = FALSE) +
  geom_text(data = cities_10, aes(x = lon.from, y = lat.from, label = from), inherit.aes = FALSE) +
  geom_segment(data = solution, aes(x = lon.from, y = lat.from, xend = lon.to,
                                    yend = lat.to), color = "blue", size = 0.3,
               arrow = arrow(), inherit.aes = FALSE)

10 C 10 Hubs min cost

equation

Show Excel
Trivial problem - 10 Cities, 2 hubs

Excel can’t do this. So we will come back to this

6 C 6 Hubs min cost

equation

Show Excel
- 6 Cities, 6 hubs

R Solution

# Choose more than two, any two

#### import data set ####
library(readr)
library(tidyr)
library(dplyr)
# Read in .csv file and create Tibble DF.
cities_raw <- read_csv("distances_my_top_50.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
# Turn into a dataframe
city_data <- as_tibble(cities_raw)
get_supply <- as_tibble(cities_raw)
# Add a number for each city 1 to 50
city_data <- city_data %>% 
  add_column(num.from = 0, .after = 4) %>% 
  add_column(num.to = 0, .after = 6)
  
# number from and to numbers
xx <- 1
for (ii in 1:50){
  for (jj in 1:50) {
    city_data$num.from[xx] <- ii
    city_data$num.to[xx] <- jj
    xx <- xx + 1
  }
}


# Choose number of cities to use
num_cities <- 6

#data <- as.data.frame(Network_Modeling)
# Get top six in each set of TO and FROM
# city_data <- city_data %>% 
#   group_by(num.from) %>%
#   slice_min(order_by = num.from, n = num_cities) %>%
#   group_by(num.to) %>%
#   slice_min(order_by = num.to, n = num_cities) %>%
#   arrange(num.from)

city_data <- city_data %>% 
  group_by(num.from) %>%
  slice_head(n = num_cities) %>% 
  group_by(num.to) %>% 
  slice_head(n = num_cities) %>% 
  group_by(num.from)
  

# redo number of cars from each city
# get supply
num_cars_month <- 4000
#library(dplyr)
get_supply <- get_supply %>% 
  slice_head(n = num_cities) %>% 
  #arrange(desc(Population)) %>% # sort Tibble by Population and descending
  #slice_head(n = 11) %>% # Get only the first n rows.
  mutate(to_pop_ratio = to_population / sum(to_population)) %>% # percent of Population
  mutate(to_num_cars = round(to_pop_ratio * num_cars_month,0)) # Calc number cars moving each month

# make into a cost matrix
cost <- city_data$cost
cost_6_city <- matrix(cost, nrow = num_cities, byrow = FALSE)


library(ompr)
library(magrittr)
library(ROI)
library(ROI.plugin.glpk)
library(ompr)
library(ompr.roi)
# Shipping Cost
# cost <- c(705.04,690.03,593.44,332.01,100.00,662.94,617.15,689.96,522.36,614.42,
#           326.04,874.85,496.92,646.68,662.94,100.00,586.57,277.47,478.96,819.49)
# cost_m <- matrix(cost, nrow = 10, byrow = FALSE)
# cost_m
# Supply to move from each cities
#supply <- as.vector(city_data$`Number of cars Shipped From`[1:6])
# the above wasn't resized for 6 cities
supply <- as.vector(get_supply$to_num_cars)

# model <- MIPModel()  %>% 
#   # Number of cars shiped from Xi to Xj
#   add_variable(x[i,j], i = 1:6, j = 1:6, type = "integer", lb = 0) %>% 
#   # Choose Houston (Y1) or Washington (Y2)
#   add_variable(y[j], j = 1:6, type = "binary") %>% 
#   #add_variable(y[j], j = 1:2, type = "integer", lb = 0, ub = 1)
#   # minimize shipping cost
#   set_objective(sum_expr(cost_6_city[i,j] * x[i,j], i = 1:6, j = 1:6), "min") %>% 
#   # must use supply from each city
#   
#   ### fix this with J's, not 1 and 2
#   #add_constraint(x[i, 1] + x[i, 2] >= supply[i], i = 1:10) #%>%
#   # FIXED! works with j's
#   add_constraint(sum_expr(x[i, j], j = 1:6) >= supply[i], i = 1:6) %>% 
#   # add this to keep Houston
#   add_constraint(y[5] == 1) %>% 
#   add_constraint(sum_expr(y[j], j = 1:6) == 2) %>% 
#   # add linking variables
#   # 1500 because the new limit should be 1224
#   add_constraint(x[i,j] <= 1500*y[j], i = 1:6, j = 1:6)
# 
# 
# #result <- ROI_solve(model, solver = "glpk")
# result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
# result
# get_solution(result, x[i,j])
# get_solution(result, y[j])


num_hubs <- 3

model <- MIPModel()  %>% 
  # Number of cars shiped from Xi to Xj
  add_variable(x[i,j], i = 1:length(supply), j = 1:length(supply), type = "integer", lb = 0) %>% 
  # Choose Houston (Y1) or Washington (Y2)
  add_variable(y[j], j = 1:length(supply), type = "binary") %>% 
  #add_variable(y[j], j = 1:2, type = "integer", lb = 0, ub = 1)
  # minimize shipping cost
  set_objective(sum_expr(cost_6_city[i,j] * x[i,j], i = 1:length(supply), j = 1:length(supply)), "min") %>% 
  # must use supply from each city
  
  ### fix this with J's, not 1 and 2
  #add_constraint(x[i, 1] + x[i, 2] >= supply[i], i = 1:10) #%>%
  # FIXED! works with j's
  add_constraint(sum_expr(x[i, j], j = 1:length(supply)) >= supply[i], i = 1:length(supply)) %>% 
  # add this to keep Houston
  add_constraint(y[5] == 1) %>% 
  add_constraint(sum_expr(y[j], j = 1:length(supply)) == num_hubs) %>% 
  # add linking variables
  # 1500 because the new limit should be 1224
  add_constraint(x[i,j] <= max(supply)*y[j], i = 1:length(supply), j = 1:length(supply))
## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.
#result <- ROI_solve(model, solver = "glpk")
result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
## <SOLVER MSG>  ----
## GLPK Simplex Optimizer, v4.65
## 44 rows, 42 columns, 115 non-zeros
##       0: obj =   0.000000000e+00 inf =   4.004e+03 (8)
##       9: obj =   1.970418398e+06 inf =   0.000e+00 (0)
## *    24: obj =   6.895753734e+05 inf =   1.359e-12 (0)
## OPTIMAL LP SOLUTION FOUND
## GLPK Integer Optimizer, v4.65
## 44 rows, 42 columns, 115 non-zeros
## 42 integer variables, 6 of which are binary
## Integer optimization begins...
## Long-step dual simplex will be used
## +    24: mip =     not found yet >=              -inf        (1; 0)
## +    33: >>>>>   1.100017285e+06 >=   8.568187925e+05  22.1% (4; 0)
## +    34: >>>>>   8.568187925e+05 >=   8.568187925e+05   0.0% (2; 3)
## +    34: mip =   8.568187925e+05 >=     tree is empty   0.0% (0; 7)
## INTEGER OPTIMAL SOLUTION FOUND
## <!SOLVER MSG> ----
result
## Status: optimal
## Objective value: 856818.8
get_solution(result, x[i,j])
##    variable i j value
## 1         x 1 1  1224
## 2         x 2 1     0
## 3         x 3 1   602
## 4         x 4 1     0
## 5         x 5 1     0
## 6         x 6 1   400
## 7         x 1 2     0
## 8         x 2 2   842
## 9         x 3 2     0
## 10        x 4 2     0
## 11        x 5 2     0
## 12        x 6 2     0
## 13        x 1 3     0
## 14        x 2 3     0
## 15        x 3 3     0
## 16        x 4 3     0
## 17        x 5 3     0
## 18        x 6 3     0
## 19        x 1 4     0
## 20        x 2 4     0
## 21        x 3 4     0
## 22        x 4 4     0
## 23        x 5 4     0
## 24        x 6 4     0
## 25        x 1 5     0
## 26        x 2 5     0
## 27        x 3 5     0
## 28        x 4 5   482
## 29        x 5 5   450
## 30        x 6 5     0
## 31        x 1 6     0
## 32        x 2 6     0
## 33        x 3 6     0
## 34        x 4 6     0
## 35        x 5 6     0
## 36        x 6 6     0
get_solution(result, y[j])
##   variable j value
## 1        y 1     1
## 2        y 2     1
## 3        y 3     0
## 4        y 4     0
## 5        y 5     1
## 6        y 6     0
#cities_10 <- read_csv("distances_top_10.csv")
solution <- as_tibble(get_solution(result, x[i,j]))
solution
## # A tibble: 36 x 4
##    variable     i     j value
##    <chr>    <int> <int> <dbl>
##  1 x            1     1  1224
##  2 x            2     1     0
##  3 x            3     1   602
##  4 x            4     1     0
##  5 x            5     1     0
##  6 x            6     1   400
##  7 x            1     2     0
##  8 x            2     2   842
##  9 x            3     2     0
## 10 x            4     2     0
## # … with 26 more rows
library(dplyr)
# get hub solution
solution_hub <- as_tibble(get_solution(result, y[j]))
to.column <- as.vector(get_supply$to)
solution_hub <- solution_hub %>% 
  add_column(Hub = 0)
solution_hub$Hub <- to.column
solution_hub
## # A tibble: 6 x 4
##   variable     j value Hub                             
##   <chr>    <int> <dbl> <chr>                           
## 1 y            1     1 New York, New York              
## 2 y            2     1 Los Angeles, California         
## 3 y            3     0 Chicago, Illinois               
## 4 y            4     0 Dallas, Texas                   
## 5 y            5     1 Houston, Texas                  
## 6 y            6     0 Washington, District of Columbia
# Adds after the second column
solution <- solution %>%
  add_column(FROM_city = 0) %>% 
  add_column(TO_city = 0) %>% 
  add_column(lon.to = 0) %>%
  add_column(lat.to = 0) %>%
  add_column(lon.from = 0) %>%
  add_column(lat.from = 0)

#m <- 1
for ( k in 1:length(city_data$lon.to)){
  solution$FROM_city[k] <- city_data$from[k]
  solution$lon.from[k] <- city_data$lon.from[k]
  solution$lat.from[k] <- city_data$lat.from[k]
  solution$TO_city[k] <- city_data$to[k]
  solution$lon.to[k] <- city_data$lon.to[k]
  solution$lat.to[k] <- city_data$lat.to[k]
  #m < m + 1

}
solution
## # A tibble: 36 x 10
##    variable     i     j value FROM_city  TO_city lon.to lat.to lon.from lat.from
##    <chr>    <int> <int> <dbl> <chr>      <chr>    <dbl>  <dbl>    <dbl>    <dbl>
##  1 x            1     1  1224 New York,… New Yo…  -74.0   40.7    -74.0     40.7
##  2 x            2     1     0 Los Angel… New Yo…  -74.0   40.7   -118.      34.1
##  3 x            3     1   602 Chicago, … New Yo…  -74.0   40.7    -87.6     41.9
##  4 x            4     1     0 Dallas, T… New Yo…  -74.0   40.7    -96.8     32.8
##  5 x            5     1     0 Houston, … New Yo…  -74.0   40.7    -95.4     29.8
##  6 x            6     1   400 Washingto… New Yo…  -74.0   40.7    -77.0     38.9
##  7 x            1     2     0 New York,… Los An… -118.    34.1    -74.0     40.7
##  8 x            2     2   842 Los Angel… Los An… -118.    34.1   -118.      34.1
##  9 x            3     2     0 Chicago, … Los An… -118.    34.1    -87.6     41.9
## 10 x            4     2     0 Dallas, T… Los An… -118.    34.1    -96.8     32.8
## # … with 26 more rows
# from.column <- c(cities_10$to[1:10])
# to.column <- c("Houston, Texas", "Washington, District of Columbia")
# m <- 1
# n <- 0
# for (k in 1:2){
#   for (l in 1:10){
#     solution$FROM_city[m] <- from.column[l]
#     solution$lon.from[m] <- cities_10$lon.to[l]
#     solution$lat.from[m] <- cities_10$lat.to[l]
#     solution$TO_city[m] <- to.column[k]
#     solution$lon.to[m] <- cities_10$lon.to[5 + n]
#     solution$lat.to[m] <- cities_10$lat.to[5 + n]
#     m <- m + 1
#   }
#   n <- n + 1
# }

### This works!!!
# no clean it up
solution <- solution %>% 
  filter(value > 0)



#### now map it ####
library(tidyverse)


# "us.cities" in maps package contains This database is of us cities of population
# greater than about 40,000. Also included are state capitals of any 
# population size.
# "state" database produces a map of the states of the United States
# mainland generated from US De- partment of the Census data
library(maps)

# Read in 10 city data with distances made in "Get Distances"
cities_10 <- read_csv("distances_top_10.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
# Get states for plotting state map
us_states <- as_tibble(map_data("state"))


ggplot(data = us_states, mapping = aes(x = long, y = lat,
                                       group = group)) +
  geom_polygon(fill= "white", color = "black") +
  geom_point(data = city_data, aes( x = lon.from, y = lat.from,
                                    size = from_population, color = "purple", alpha = 0.5),
             inherit.aes = FALSE) +
  geom_text(data = city_data, aes(x = lon.from, y = lat.from, label = from), inherit.aes = FALSE) +
  geom_segment(data = solution, aes(x = lon.from, y = lat.from, xend = lon.to,
                                    yend = lat.to), color = "blue", size = 0.3,
               arrow = arrow(), inherit.aes = FALSE)

no we can’t really do much more in Excel with the internal solver. There are commercial solvers that can do it. But notice that it is a lot of work to keep adding each city to each hub path.

back to 10 C 10 H

Let’s 10 C, best 2 hubs, with 1 Houston

# Choose more than two, any two

#### import data set ####
library(readr)
library(tidyr)
library(dplyr)
# Read in .csv file and create Tibble DF.
cities_raw <- read_csv("distances_my_top_50.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
# Turn into a dataframe
city_data <- as_tibble(cities_raw)
get_supply <- as_tibble(cities_raw)
# Add a number for each city 1 to 50
city_data <- city_data %>% 
  add_column(num.from = 0, .after = 4) %>% 
  add_column(num.to = 0, .after = 6)
  
# number from and to numbers
xx <- 1
for (ii in 1:50){
  for (jj in 1:50) {
    city_data$num.from[xx] <- ii
    city_data$num.to[xx] <- jj
    xx <- xx + 1
  }
}


# Choose number of cities to use
num_cities <- 10

#data <- as.data.frame(Network_Modeling)
# Get top six in each set of TO and FROM
# city_data <- city_data %>% 
#   group_by(num.from) %>%
#   slice_min(order_by = num.from, n = num_cities) %>%
#   group_by(num.to) %>%
#   slice_min(order_by = num.to, n = num_cities) %>%
#   arrange(num.from)

city_data <- city_data %>% 
  group_by(num.from) %>%
  slice_head(n = num_cities) %>% 
  group_by(num.to) %>% 
  slice_head(n = num_cities) %>% 
  group_by(num.from)
  

# redo number of cars from each city
# get supply
num_cars_month <- 4000
#library(dplyr)
get_supply <- get_supply %>% 
  slice_head(n = num_cities) %>% 
  #arrange(desc(Population)) %>% # sort Tibble by Population and descending
  #slice_head(n = 11) %>% # Get only the first n rows.
  mutate(to_pop_ratio = to_population / sum(to_population)) %>% # percent of Population
  mutate(to_num_cars = round(to_pop_ratio * num_cars_month,0)) # Calc number cars moving each month

# make into a cost matrix
cost <- city_data$cost
cost_6_city <- matrix(cost, nrow = num_cities, byrow = FALSE)


library(ompr)
library(magrittr)
library(ROI)
library(ROI.plugin.glpk)
library(ompr)
library(ompr.roi)
# Shipping Cost
# cost <- c(705.04,690.03,593.44,332.01,100.00,662.94,617.15,689.96,522.36,614.42,
#           326.04,874.85,496.92,646.68,662.94,100.00,586.57,277.47,478.96,819.49)
# cost_m <- matrix(cost, nrow = 10, byrow = FALSE)
# cost_m
# Supply to move from each cities
#supply <- as.vector(city_data$`Number of cars Shipped From`[1:6])
# the above wasn't resized for 6 cities
supply <- as.vector(get_supply$to_num_cars)

# model <- MIPModel()  %>% 
#   # Number of cars shiped from Xi to Xj
#   add_variable(x[i,j], i = 1:6, j = 1:6, type = "integer", lb = 0) %>% 
#   # Choose Houston (Y1) or Washington (Y2)
#   add_variable(y[j], j = 1:6, type = "binary") %>% 
#   #add_variable(y[j], j = 1:2, type = "integer", lb = 0, ub = 1)
#   # minimize shipping cost
#   set_objective(sum_expr(cost_6_city[i,j] * x[i,j], i = 1:6, j = 1:6), "min") %>% 
#   # must use supply from each city
#   
#   ### fix this with J's, not 1 and 2
#   #add_constraint(x[i, 1] + x[i, 2] >= supply[i], i = 1:10) #%>%
#   # FIXED! works with j's
#   add_constraint(sum_expr(x[i, j], j = 1:6) >= supply[i], i = 1:6) %>% 
#   # add this to keep Houston
#   add_constraint(y[5] == 1) %>% 
#   add_constraint(sum_expr(y[j], j = 1:6) == 2) %>% 
#   # add linking variables
#   # 1500 because the new limit should be 1224
#   add_constraint(x[i,j] <= 1500*y[j], i = 1:6, j = 1:6)
# 
# 
# #result <- ROI_solve(model, solver = "glpk")
# result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
# result
# get_solution(result, x[i,j])
# get_solution(result, y[j])


num_hubs <- 2

model <- MIPModel()  %>% 
  # Number of cars shiped from Xi to Xj
  add_variable(x[i,j], i = 1:length(supply), j = 1:length(supply), type = "integer", lb = 0) %>% 
  # Choose Houston (Y1) or Washington (Y2)
  add_variable(y[j], j = 1:length(supply), type = "binary") %>% 
  #add_variable(y[j], j = 1:2, type = "integer", lb = 0, ub = 1)
  # minimize shipping cost
  set_objective(sum_expr(cost_6_city[i,j] * x[i,j], i = 1:length(supply), j = 1:length(supply)), "min") %>% 
  # must use supply from each city
  
  ### fix this with J's, not 1 and 2
  #add_constraint(x[i, 1] + x[i, 2] >= supply[i], i = 1:10) #%>%
  # FIXED! works with j's
  add_constraint(sum_expr(x[i, j], j = 1:length(supply)) >= supply[i], i = 1:length(supply)) %>% 
  # add this to keep Houston
  add_constraint(y[5] == 1) %>% 
  add_constraint(sum_expr(y[j], j = 1:length(supply)) == num_hubs) %>% 
  # add linking variables
  # 1500 because the new limit should be 1224
  add_constraint(x[i,j] <= max(supply)*y[j], i = 1:length(supply), j = 1:length(supply))
## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.
#result <- ROI_solve(model, solver = "glpk")
result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
## <SOLVER MSG>  ----
## GLPK Simplex Optimizer, v4.65
## 112 rows, 110 columns, 311 non-zeros
##       0: obj =   0.000000000e+00 inf =   4.003e+03 (12)
##      12: obj =   2.035994388e+06 inf =   0.000e+00 (0)
## *    47: obj =   1.421579828e+06 inf =   0.000e+00 (0)
## OPTIMAL LP SOLUTION FOUND
## GLPK Integer Optimizer, v4.65
## 112 rows, 110 columns, 311 non-zeros
## 110 integer variables, 10 of which are binary
## Integer optimization begins...
## Long-step dual simplex will be used
## +    47: mip =     not found yet >=              -inf        (1; 0)
## +    78: >>>>>   2.015425696e+06 >=   1.478878062e+06  26.6% (6; 0)
## +    95: >>>>>   1.904081429e+06 >=   1.511521912e+06  20.6% (5; 1)
## +   116: >>>>>   1.523111984e+06 >=   1.523111984e+06   0.0% (5; 3)
## +   116: mip =   1.523111984e+06 >=     tree is empty   0.0% (0; 15)
## INTEGER OPTIMAL SOLUTION FOUND
## <!SOLVER MSG> ----
result
## Status: optimal
## Objective value: 1523112
get_solution(result, x[i,j])
##     variable  i  j value
## 1          x  1  1   893
## 2          x  2  1     0
## 3          x  3  1   440
## 4          x  4  1     0
## 5          x  5  1     0
## 6          x  6  1   292
## 7          x  7  1     0
## 8          x  8  1   284
## 9          x  9  1     0
## 10         x 10  1     0
## 11         x  1  2     0
## 12         x  2  2     0
## 13         x  3  2     0
## 14         x  4  2     0
## 15         x  5  2     0
## 16         x  6  2     0
## 17         x  7  2     0
## 18         x  8  2     0
## 19         x  9  2     0
## 20         x 10  2     0
## 21         x  1  3     0
## 22         x  2  3     0
## 23         x  3  3     0
## 24         x  4  3     0
## 25         x  5  3     0
## 26         x  6  3     0
## 27         x  7  3     0
## 28         x  8  3     0
## 29         x  9  3     0
## 30         x 10  3     0
## 31         x  1  4     0
## 32         x  2  4     0
## 33         x  3  4     0
## 34         x  4  4     0
## 35         x  5  4     0
## 36         x  6  4     0
## 37         x  7  4     0
## 38         x  8  4     0
## 39         x  9  4     0
## 40         x 10  4     0
## 41         x  1  5     0
## 42         x  2  5   614
## 43         x  3  5     0
## 44         x  4  5   352
## 45         x  5  5   328
## 46         x  6  5     0
## 47         x  7  5   287
## 48         x  8  5     0
## 49         x  9  5   280
## 50         x 10  5   230
## 51         x  1  6     0
## 52         x  2  6     0
## 53         x  3  6     0
## 54         x  4  6     0
## 55         x  5  6     0
## 56         x  6  6     0
## 57         x  7  6     0
## 58         x  8  6     0
## 59         x  9  6     0
## 60         x 10  6     0
## 61         x  1  7     0
## 62         x  2  7     0
## 63         x  3  7     0
## 64         x  4  7     0
## 65         x  5  7     0
## 66         x  6  7     0
## 67         x  7  7     0
## 68         x  8  7     0
## 69         x  9  7     0
## 70         x 10  7     0
## 71         x  1  8     0
## 72         x  2  8     0
## 73         x  3  8     0
## 74         x  4  8     0
## 75         x  5  8     0
## 76         x  6  8     0
## 77         x  7  8     0
## 78         x  8  8     0
## 79         x  9  8     0
## 80         x 10  8     0
## 81         x  1  9     0
## 82         x  2  9     0
## 83         x  3  9     0
## 84         x  4  9     0
## 85         x  5  9     0
## 86         x  6  9     0
## 87         x  7  9     0
## 88         x  8  9     0
## 89         x  9  9     0
## 90         x 10  9     0
## 91         x  1 10     0
## 92         x  2 10     0
## 93         x  3 10     0
## 94         x  4 10     0
## 95         x  5 10     0
## 96         x  6 10     0
## 97         x  7 10     0
## 98         x  8 10     0
## 99         x  9 10     0
## 100        x 10 10     0
get_solution(result, y[j])
##    variable  j value
## 1         y  1     1
## 2         y  2     0
## 3         y  3     0
## 4         y  4     0
## 5         y  5     1
## 6         y  6     0
## 7         y  7     0
## 8         y  8     0
## 9         y  9     0
## 10        y 10     0
#cities_10 <- read_csv("distances_top_10.csv")
solution <- as_tibble(get_solution(result, x[i,j]))
solution
## # A tibble: 100 x 4
##    variable     i     j value
##    <chr>    <int> <int> <dbl>
##  1 x            1     1   893
##  2 x            2     1     0
##  3 x            3     1   440
##  4 x            4     1     0
##  5 x            5     1     0
##  6 x            6     1   292
##  7 x            7     1     0
##  8 x            8     1   284
##  9 x            9     1     0
## 10 x           10     1     0
## # … with 90 more rows
library(dplyr)
# get hub solution
solution_hub <- as_tibble(get_solution(result, y[j]))
to.column <- as.vector(get_supply$to)
solution_hub <- solution_hub %>% 
  add_column(Hub = 0)
solution_hub$Hub <- to.column
solution_hub
## # A tibble: 10 x 4
##    variable     j value Hub                             
##    <chr>    <int> <dbl> <chr>                           
##  1 y            1     1 New York, New York              
##  2 y            2     0 Los Angeles, California         
##  3 y            3     0 Chicago, Illinois               
##  4 y            4     0 Dallas, Texas                   
##  5 y            5     1 Houston, Texas                  
##  6 y            6     0 Washington, District of Columbia
##  7 y            7     0 Miami, Florida                  
##  8 y            8     0 Philadelphia, Pennsylvania      
##  9 y            9     0 Atlanta, Georgia                
## 10 y           10     0 Phoenix, Arizona
# Adds after the second column
solution <- solution %>%
  add_column(FROM_city = 0) %>% 
  add_column(TO_city = 0) %>% 
  add_column(lon.to = 0) %>%
  add_column(lat.to = 0) %>%
  add_column(lon.from = 0) %>%
  add_column(lat.from = 0)

#m <- 1
for ( k in 1:length(city_data$lon.to)){
  solution$FROM_city[k] <- city_data$from[k]
  solution$lon.from[k] <- city_data$lon.from[k]
  solution$lat.from[k] <- city_data$lat.from[k]
  solution$TO_city[k] <- city_data$to[k]
  solution$lon.to[k] <- city_data$lon.to[k]
  solution$lat.to[k] <- city_data$lat.to[k]
  #m < m + 1

}
solution
## # A tibble: 100 x 10
##    variable     i     j value FROM_city  TO_city lon.to lat.to lon.from lat.from
##    <chr>    <int> <int> <dbl> <chr>      <chr>    <dbl>  <dbl>    <dbl>    <dbl>
##  1 x            1     1   893 New York,… New Yo…  -74.0   40.7    -74.0     40.7
##  2 x            2     1     0 Los Angel… New Yo…  -74.0   40.7   -118.      34.1
##  3 x            3     1   440 Chicago, … New Yo…  -74.0   40.7    -87.6     41.9
##  4 x            4     1     0 Dallas, T… New Yo…  -74.0   40.7    -96.8     32.8
##  5 x            5     1     0 Houston, … New Yo…  -74.0   40.7    -95.4     29.8
##  6 x            6     1   292 Washingto… New Yo…  -74.0   40.7    -77.0     38.9
##  7 x            7     1     0 Miami, Fl… New Yo…  -74.0   40.7    -80.2     25.8
##  8 x            8     1   284 Philadelp… New Yo…  -74.0   40.7    -75.2     40.0
##  9 x            9     1     0 Atlanta, … New Yo…  -74.0   40.7    -84.4     33.7
## 10 x           10     1     0 Phoenix, … New Yo…  -74.0   40.7   -112.      33.4
## # … with 90 more rows
# from.column <- c(cities_10$to[1:10])
# to.column <- c("Houston, Texas", "Washington, District of Columbia")
# m <- 1
# n <- 0
# for (k in 1:2){
#   for (l in 1:10){
#     solution$FROM_city[m] <- from.column[l]
#     solution$lon.from[m] <- cities_10$lon.to[l]
#     solution$lat.from[m] <- cities_10$lat.to[l]
#     solution$TO_city[m] <- to.column[k]
#     solution$lon.to[m] <- cities_10$lon.to[5 + n]
#     solution$lat.to[m] <- cities_10$lat.to[5 + n]
#     m <- m + 1
#   }
#   n <- n + 1
# }

### This works!!!
# no clean it up
solution <- solution %>% 
  filter(value > 0)



#### now map it ####
library(tidyverse)


# "us.cities" in maps package contains This database is of us cities of population
# greater than about 40,000. Also included are state capitals of any 
# population size.
# "state" database produces a map of the states of the United States
# mainland generated from US De- partment of the Census data
library(maps)

# Read in 10 city data with distances made in "Get Distances"
cities_10 <- read_csv("distances_top_10.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
# Get states for plotting state map
us_states <- as_tibble(map_data("state"))


ggplot(data = us_states, mapping = aes(x = long, y = lat,
                                       group = group)) +
  geom_polygon(fill= "white", color = "black") +
  geom_point(data = city_data, aes( x = lon.from, y = lat.from,
                                    size = from_population, color = "purple", alpha = 0.5),
             inherit.aes = FALSE) +
  geom_text(data = city_data, aes(x = lon.from, y = lat.from, label = from), inherit.aes = FALSE) +
  geom_segment(data = solution, aes(x = lon.from, y = lat.from, xend = lon.to,
                                    yend = lat.to), color = "blue", size = 0.3,
               arrow = arrow(), inherit.aes = FALSE)

back to 10 C 10 H

Let’s 10 C, best 2 hubs, any hubs

# Choose more than two, any two

#### import data set ####
library(readr)
library(tidyr)
library(dplyr)
# Read in .csv file and create Tibble DF.
cities_raw <- read_csv("distances_my_top_50.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
# Turn into a dataframe
city_data <- as_tibble(cities_raw)
get_supply <- as_tibble(cities_raw)
# Add a number for each city 1 to 50
city_data <- city_data %>% 
  add_column(num.from = 0, .after = 4) %>% 
  add_column(num.to = 0, .after = 6)
  
# number from and to numbers
xx <- 1
for (ii in 1:50){
  for (jj in 1:50) {
    city_data$num.from[xx] <- ii
    city_data$num.to[xx] <- jj
    xx <- xx + 1
  }
}


# Choose number of cities to use
num_cities <- 10

#data <- as.data.frame(Network_Modeling)
# Get top six in each set of TO and FROM
# city_data <- city_data %>% 
#   group_by(num.from) %>%
#   slice_min(order_by = num.from, n = num_cities) %>%
#   group_by(num.to) %>%
#   slice_min(order_by = num.to, n = num_cities) %>%
#   arrange(num.from)

city_data <- city_data %>% 
  group_by(num.from) %>%
  slice_head(n = num_cities) %>% 
  group_by(num.to) %>% 
  slice_head(n = num_cities) %>% 
  group_by(num.from)
  

# redo number of cars from each city
# get supply
num_cars_month <- 4000
#library(dplyr)
get_supply <- get_supply %>% 
  slice_head(n = num_cities) %>% 
  #arrange(desc(Population)) %>% # sort Tibble by Population and descending
  #slice_head(n = 11) %>% # Get only the first n rows.
  mutate(to_pop_ratio = to_population / sum(to_population)) %>% # percent of Population
  mutate(to_num_cars = round(to_pop_ratio * num_cars_month,0)) # Calc number cars moving each month

# make into a cost matrix
cost <- city_data$cost
cost_6_city <- matrix(cost, nrow = num_cities, byrow = FALSE)


library(ompr)
library(magrittr)
library(ROI)
library(ROI.plugin.glpk)
library(ompr)
library(ompr.roi)
# Shipping Cost
# cost <- c(705.04,690.03,593.44,332.01,100.00,662.94,617.15,689.96,522.36,614.42,
#           326.04,874.85,496.92,646.68,662.94,100.00,586.57,277.47,478.96,819.49)
# cost_m <- matrix(cost, nrow = 10, byrow = FALSE)
# cost_m
# Supply to move from each cities
#supply <- as.vector(city_data$`Number of cars Shipped From`[1:6])
# the above wasn't resized for 6 cities
supply <- as.vector(get_supply$to_num_cars)

# model <- MIPModel()  %>% 
#   # Number of cars shiped from Xi to Xj
#   add_variable(x[i,j], i = 1:6, j = 1:6, type = "integer", lb = 0) %>% 
#   # Choose Houston (Y1) or Washington (Y2)
#   add_variable(y[j], j = 1:6, type = "binary") %>% 
#   #add_variable(y[j], j = 1:2, type = "integer", lb = 0, ub = 1)
#   # minimize shipping cost
#   set_objective(sum_expr(cost_6_city[i,j] * x[i,j], i = 1:6, j = 1:6), "min") %>% 
#   # must use supply from each city
#   
#   ### fix this with J's, not 1 and 2
#   #add_constraint(x[i, 1] + x[i, 2] >= supply[i], i = 1:10) #%>%
#   # FIXED! works with j's
#   add_constraint(sum_expr(x[i, j], j = 1:6) >= supply[i], i = 1:6) %>% 
#   # add this to keep Houston
#   add_constraint(y[5] == 1) %>% 
#   add_constraint(sum_expr(y[j], j = 1:6) == 2) %>% 
#   # add linking variables
#   # 1500 because the new limit should be 1224
#   add_constraint(x[i,j] <= 1500*y[j], i = 1:6, j = 1:6)
# 
# 
# #result <- ROI_solve(model, solver = "glpk")
# result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
# result
# get_solution(result, x[i,j])
# get_solution(result, y[j])


num_hubs <- 2

model <- MIPModel()  %>% 
  # Number of cars shiped from Xi to Xj
  add_variable(x[i,j], i = 1:length(supply), j = 1:length(supply), type = "integer", lb = 0) %>% 
  # Choose Houston (Y1) or Washington (Y2)
  add_variable(y[j], j = 1:length(supply), type = "binary") %>% 
  #add_variable(y[j], j = 1:2, type = "integer", lb = 0, ub = 1)
  # minimize shipping cost
  set_objective(sum_expr(cost_6_city[i,j] * x[i,j], i = 1:length(supply), j = 1:length(supply)), "min") %>% 
  # must use supply from each city
  
  ### fix this with J's, not 1 and 2
  #add_constraint(x[i, 1] + x[i, 2] >= supply[i], i = 1:10) #%>%
  # FIXED! works with j's
  add_constraint(sum_expr(x[i, j], j = 1:length(supply)) >= supply[i], i = 1:length(supply)) %>% 
  # add this to keep Houston
  #add_constraint(y[5] == 1) %>% 
  add_constraint(sum_expr(y[j], j = 1:length(supply)) == num_hubs) %>% 
  # add linking variables
  # 1500 because the new limit should be 1224
  add_constraint(x[i,j] <= max(supply)*y[j], i = 1:length(supply), j = 1:length(supply))
## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.
#result <- ROI_solve(model, solver = "glpk")
result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
## <SOLVER MSG>  ----
## GLPK Simplex Optimizer, v4.65
## 111 rows, 110 columns, 310 non-zeros
##       0: obj =   0.000000000e+00 inf =   4.002e+03 (11)
##      12: obj =   2.035994388e+06 inf =   0.000e+00 (0)
## *    50: obj =   1.088161077e+06 inf =   0.000e+00 (0)
## OPTIMAL LP SOLUTION FOUND
## GLPK Integer Optimizer, v4.65
## 111 rows, 110 columns, 310 non-zeros
## 110 integer variables, 10 of which are binary
## Integer optimization begins...
## Long-step dual simplex will be used
## +    50: mip =     not found yet >=              -inf        (1; 0)
## +    90: >>>>>   1.490837287e+06 >=   1.147800185e+06  23.0% (9; 0)
## +   185: >>>>>   1.432223155e+06 >=   1.272424861e+06  11.2% (10; 8)
## +   247: mip =   1.432223155e+06 >=     tree is empty   0.0% (0; 33)
## INTEGER OPTIMAL SOLUTION FOUND
## <!SOLVER MSG> ----
result
## Status: optimal
## Objective value: 1432223
get_solution(result, x[i,j])
##     variable  i  j value
## 1          x  1  1   893
## 2          x  2  1     0
## 3          x  3  1   440
## 4          x  4  1     0
## 5          x  5  1     0
## 6          x  6  1   292
## 7          x  7  1   287
## 8          x  8  1   284
## 9          x  9  1   280
## 10         x 10  1     0
## 11         x  1  2     0
## 12         x  2  2   614
## 13         x  3  2     0
## 14         x  4  2   352
## 15         x  5  2   328
## 16         x  6  2     0
## 17         x  7  2     0
## 18         x  8  2     0
## 19         x  9  2     0
## 20         x 10  2   230
## 21         x  1  3     0
## 22         x  2  3     0
## 23         x  3  3     0
## 24         x  4  3     0
## 25         x  5  3     0
## 26         x  6  3     0
## 27         x  7  3     0
## 28         x  8  3     0
## 29         x  9  3     0
## 30         x 10  3     0
## 31         x  1  4     0
## 32         x  2  4     0
## 33         x  3  4     0
## 34         x  4  4     0
## 35         x  5  4     0
## 36         x  6  4     0
## 37         x  7  4     0
## 38         x  8  4     0
## 39         x  9  4     0
## 40         x 10  4     0
## 41         x  1  5     0
## 42         x  2  5     0
## 43         x  3  5     0
## 44         x  4  5     0
## 45         x  5  5     0
## 46         x  6  5     0
## 47         x  7  5     0
## 48         x  8  5     0
## 49         x  9  5     0
## 50         x 10  5     0
## 51         x  1  6     0
## 52         x  2  6     0
## 53         x  3  6     0
## 54         x  4  6     0
## 55         x  5  6     0
## 56         x  6  6     0
## 57         x  7  6     0
## 58         x  8  6     0
## 59         x  9  6     0
## 60         x 10  6     0
## 61         x  1  7     0
## 62         x  2  7     0
## 63         x  3  7     0
## 64         x  4  7     0
## 65         x  5  7     0
## 66         x  6  7     0
## 67         x  7  7     0
## 68         x  8  7     0
## 69         x  9  7     0
## 70         x 10  7     0
## 71         x  1  8     0
## 72         x  2  8     0
## 73         x  3  8     0
## 74         x  4  8     0
## 75         x  5  8     0
## 76         x  6  8     0
## 77         x  7  8     0
## 78         x  8  8     0
## 79         x  9  8     0
## 80         x 10  8     0
## 81         x  1  9     0
## 82         x  2  9     0
## 83         x  3  9     0
## 84         x  4  9     0
## 85         x  5  9     0
## 86         x  6  9     0
## 87         x  7  9     0
## 88         x  8  9     0
## 89         x  9  9     0
## 90         x 10  9     0
## 91         x  1 10     0
## 92         x  2 10     0
## 93         x  3 10     0
## 94         x  4 10     0
## 95         x  5 10     0
## 96         x  6 10     0
## 97         x  7 10     0
## 98         x  8 10     0
## 99         x  9 10     0
## 100        x 10 10     0
get_solution(result, y[j])
##    variable  j value
## 1         y  1     1
## 2         y  2     1
## 3         y  3     0
## 4         y  4     0
## 5         y  5     0
## 6         y  6     0
## 7         y  7     0
## 8         y  8     0
## 9         y  9     0
## 10        y 10     0
#cities_10 <- read_csv("distances_top_10.csv")
solution <- as_tibble(get_solution(result, x[i,j]))
solution
## # A tibble: 100 x 4
##    variable     i     j value
##    <chr>    <int> <int> <dbl>
##  1 x            1     1   893
##  2 x            2     1     0
##  3 x            3     1   440
##  4 x            4     1     0
##  5 x            5     1     0
##  6 x            6     1   292
##  7 x            7     1   287
##  8 x            8     1   284
##  9 x            9     1   280
## 10 x           10     1     0
## # … with 90 more rows
library(dplyr)
# get hub solution
solution_hub <- as_tibble(get_solution(result, y[j]))
to.column <- as.vector(get_supply$to)
solution_hub <- solution_hub %>% 
  add_column(Hub = 0)
solution_hub$Hub <- to.column
solution_hub
## # A tibble: 10 x 4
##    variable     j value Hub                             
##    <chr>    <int> <dbl> <chr>                           
##  1 y            1     1 New York, New York              
##  2 y            2     1 Los Angeles, California         
##  3 y            3     0 Chicago, Illinois               
##  4 y            4     0 Dallas, Texas                   
##  5 y            5     0 Houston, Texas                  
##  6 y            6     0 Washington, District of Columbia
##  7 y            7     0 Miami, Florida                  
##  8 y            8     0 Philadelphia, Pennsylvania      
##  9 y            9     0 Atlanta, Georgia                
## 10 y           10     0 Phoenix, Arizona
# Adds after the second column
solution <- solution %>%
  add_column(FROM_city = 0) %>% 
  add_column(TO_city = 0) %>% 
  add_column(lon.to = 0) %>%
  add_column(lat.to = 0) %>%
  add_column(lon.from = 0) %>%
  add_column(lat.from = 0)

#m <- 1
for ( k in 1:length(city_data$lon.to)){
  solution$FROM_city[k] <- city_data$from[k]
  solution$lon.from[k] <- city_data$lon.from[k]
  solution$lat.from[k] <- city_data$lat.from[k]
  solution$TO_city[k] <- city_data$to[k]
  solution$lon.to[k] <- city_data$lon.to[k]
  solution$lat.to[k] <- city_data$lat.to[k]
  #m < m + 1

}
solution
## # A tibble: 100 x 10
##    variable     i     j value FROM_city  TO_city lon.to lat.to lon.from lat.from
##    <chr>    <int> <int> <dbl> <chr>      <chr>    <dbl>  <dbl>    <dbl>    <dbl>
##  1 x            1     1   893 New York,… New Yo…  -74.0   40.7    -74.0     40.7
##  2 x            2     1     0 Los Angel… New Yo…  -74.0   40.7   -118.      34.1
##  3 x            3     1   440 Chicago, … New Yo…  -74.0   40.7    -87.6     41.9
##  4 x            4     1     0 Dallas, T… New Yo…  -74.0   40.7    -96.8     32.8
##  5 x            5     1     0 Houston, … New Yo…  -74.0   40.7    -95.4     29.8
##  6 x            6     1   292 Washingto… New Yo…  -74.0   40.7    -77.0     38.9
##  7 x            7     1   287 Miami, Fl… New Yo…  -74.0   40.7    -80.2     25.8
##  8 x            8     1   284 Philadelp… New Yo…  -74.0   40.7    -75.2     40.0
##  9 x            9     1   280 Atlanta, … New Yo…  -74.0   40.7    -84.4     33.7
## 10 x           10     1     0 Phoenix, … New Yo…  -74.0   40.7   -112.      33.4
## # … with 90 more rows
# from.column <- c(cities_10$to[1:10])
# to.column <- c("Houston, Texas", "Washington, District of Columbia")
# m <- 1
# n <- 0
# for (k in 1:2){
#   for (l in 1:10){
#     solution$FROM_city[m] <- from.column[l]
#     solution$lon.from[m] <- cities_10$lon.to[l]
#     solution$lat.from[m] <- cities_10$lat.to[l]
#     solution$TO_city[m] <- to.column[k]
#     solution$lon.to[m] <- cities_10$lon.to[5 + n]
#     solution$lat.to[m] <- cities_10$lat.to[5 + n]
#     m <- m + 1
#   }
#   n <- n + 1
# }

### This works!!!
# no clean it up
solution <- solution %>% 
  filter(value > 0)



#### now map it ####
library(tidyverse)


# "us.cities" in maps package contains This database is of us cities of population
# greater than about 40,000. Also included are state capitals of any 
# population size.
# "state" database produces a map of the states of the United States
# mainland generated from US De- partment of the Census data
library(maps)

# Read in 10 city data with distances made in "Get Distances"
cities_10 <- read_csv("distances_top_10.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
# Get states for plotting state map
us_states <- as_tibble(map_data("state"))


ggplot(data = us_states, mapping = aes(x = long, y = lat,
                                       group = group)) +
  geom_polygon(fill= "white", color = "black") +
  geom_point(data = city_data, aes( x = lon.from, y = lat.from,
                                    size = from_population, color = "purple", alpha = 0.5),
             inherit.aes = FALSE) +
  geom_text(data = city_data, aes(x = lon.from, y = lat.from, label = from), inherit.aes = FALSE) +
  geom_segment(data = solution, aes(x = lon.from, y = lat.from, xend = lon.to,
                                    yend = lat.to), color = "blue", size = 0.3,
               arrow = arrow(), inherit.aes = FALSE)

equation

R solution # now we are cooking # now 50 cities and X number of hubs

Let’s 50 C, best 2 hubs, with 1 Houston

# Choose more than two, any two

#### import data set ####
library(readr)
library(tidyr)
library(dplyr)
# Read in .csv file and create Tibble DF.
cities_raw <- read_csv("distances_my_top_50.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
# Turn into a dataframe
city_data <- as_tibble(cities_raw)
get_supply <- as_tibble(cities_raw)
# Add a number for each city 1 to 50
city_data <- city_data %>% 
  add_column(num.from = 0, .after = 4) %>% 
  add_column(num.to = 0, .after = 6)
  
# number from and to numbers
xx <- 1
for (ii in 1:50){
  for (jj in 1:50) {
    city_data$num.from[xx] <- ii
    city_data$num.to[xx] <- jj
    xx <- xx + 1
  }
}


# Choose number of cities to use
num_cities <- 50

#data <- as.data.frame(Network_Modeling)
# Get top six in each set of TO and FROM
# city_data <- city_data %>% 
#   group_by(num.from) %>%
#   slice_min(order_by = num.from, n = num_cities) %>%
#   group_by(num.to) %>%
#   slice_min(order_by = num.to, n = num_cities) %>%
#   arrange(num.from)

city_data <- city_data %>% 
  group_by(num.from) %>%
  slice_head(n = num_cities) %>% 
  group_by(num.to) %>% 
  slice_head(n = num_cities) %>% 
  group_by(num.from)
  

# redo number of cars from each city
# get supply
num_cars_month <- 4000
#library(dplyr)
get_supply <- get_supply %>% 
  slice_head(n = num_cities) %>% 
  #arrange(desc(Population)) %>% # sort Tibble by Population and descending
  #slice_head(n = 11) %>% # Get only the first n rows.
  mutate(to_pop_ratio = to_population / sum(to_population)) %>% # percent of Population
  mutate(to_num_cars = round(to_pop_ratio * num_cars_month,0)) # Calc number cars moving each month

# make into a cost matrix
cost <- city_data$cost
cost_6_city <- matrix(cost, nrow = num_cities, byrow = FALSE)


library(ompr)
library(magrittr)
library(ROI)
library(ROI.plugin.glpk)
library(ompr)
library(ompr.roi)
# Shipping Cost
# cost <- c(705.04,690.03,593.44,332.01,100.00,662.94,617.15,689.96,522.36,614.42,
#           326.04,874.85,496.92,646.68,662.94,100.00,586.57,277.47,478.96,819.49)
# cost_m <- matrix(cost, nrow = 10, byrow = FALSE)
# cost_m
# Supply to move from each cities
#supply <- as.vector(city_data$`Number of cars Shipped From`[1:6])
# the above wasn't resized for 6 cities
supply <- as.vector(get_supply$to_num_cars)

# model <- MIPModel()  %>% 
#   # Number of cars shiped from Xi to Xj
#   add_variable(x[i,j], i = 1:6, j = 1:6, type = "integer", lb = 0) %>% 
#   # Choose Houston (Y1) or Washington (Y2)
#   add_variable(y[j], j = 1:6, type = "binary") %>% 
#   #add_variable(y[j], j = 1:2, type = "integer", lb = 0, ub = 1)
#   # minimize shipping cost
#   set_objective(sum_expr(cost_6_city[i,j] * x[i,j], i = 1:6, j = 1:6), "min") %>% 
#   # must use supply from each city
#   
#   ### fix this with J's, not 1 and 2
#   #add_constraint(x[i, 1] + x[i, 2] >= supply[i], i = 1:10) #%>%
#   # FIXED! works with j's
#   add_constraint(sum_expr(x[i, j], j = 1:6) >= supply[i], i = 1:6) %>% 
#   # add this to keep Houston
#   add_constraint(y[5] == 1) %>% 
#   add_constraint(sum_expr(y[j], j = 1:6) == 2) %>% 
#   # add linking variables
#   # 1500 because the new limit should be 1224
#   add_constraint(x[i,j] <= 1500*y[j], i = 1:6, j = 1:6)
# 
# 
# #result <- ROI_solve(model, solver = "glpk")
# result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
# result
# get_solution(result, x[i,j])
# get_solution(result, y[j])


num_hubs <- 2

model <- MIPModel()  %>% 
  # Number of cars shiped from Xi to Xj
  add_variable(x[i,j], i = 1:length(supply), j = 1:length(supply), type = "integer", lb = 0) %>% 
  # Choose Houston (Y1) or Washington (Y2)
  add_variable(y[j], j = 1:length(supply), type = "binary") %>% 
  #add_variable(y[j], j = 1:2, type = "integer", lb = 0, ub = 1)
  # minimize shipping cost
  set_objective(sum_expr(cost_6_city[i,j] * x[i,j], i = 1:length(supply), j = 1:length(supply)), "min") %>% 
  # must use supply from each city
  
  ### fix this with J's, not 1 and 2
  #add_constraint(x[i, 1] + x[i, 2] >= supply[i], i = 1:10) #%>%
  # FIXED! works with j's
  add_constraint(sum_expr(x[i, j], j = 1:length(supply)) >= supply[i], i = 1:length(supply)) %>% 
  # add this to keep Houston
  add_constraint(y[5] == 1) %>% 
  add_constraint(sum_expr(y[j], j = 1:length(supply)) == num_hubs) %>% 
  # add linking variables
  # 1500 because the new limit should be 1224
  add_constraint(x[i,j] <= max(supply)*y[j], i = 1:length(supply), j = 1:length(supply))
## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.
#result <- ROI_solve(model, solver = "glpk")
result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
## <SOLVER MSG>  ----
## GLPK Simplex Optimizer, v4.65
## 2552 rows, 2550 columns, 7551 non-zeros
##       0: obj =   0.000000000e+00 inf =   4.005e+03 (52)
##      52: obj =   2.229404654e+06 inf =   0.000e+00 (0)
## *   591: obj =   1.437028710e+06 inf =   0.000e+00 (0) 1
## OPTIMAL LP SOLUTION FOUND
## GLPK Integer Optimizer, v4.65
## 2552 rows, 2550 columns, 7551 non-zeros
## 2550 integer variables, 50 of which are binary
## Integer optimization begins...
## Long-step dual simplex will be used
## +   591: mip =     not found yet >=              -inf        (1; 0)
## +  1384: >>>>>   2.131345151e+06 >=   1.450222914e+06  32.0% (29; 0)
## +  1622: >>>>>   1.940727250e+06 >=   1.456125967e+06  25.0% (28; 1)
## +  1847: >>>>>   1.900875949e+06 >=   1.456965099e+06  23.4% (27; 2)
## +  2065: >>>>>   1.846705947e+06 >=   1.458662419e+06  21.0% (26; 3)
## +  2597: >>>>>   1.846506687e+06 >=   1.467178340e+06  20.5% (23; 6)
## +  3009: >>>>>   1.845355183e+06 >=   1.475032620e+06  20.1% (21; 8)
## +  3205: >>>>>   1.824952889e+06 >=   1.475888345e+06  19.1% (20; 9)
## +  7780: mip =   1.824952889e+06 >=     tree is empty   0.0% (0; 79)
## INTEGER OPTIMAL SOLUTION FOUND
## <!SOLVER MSG> ----
result
## Status: optimal
## Objective value: 1824953
get_solution(result, x[i,j])
##      variable  i  j value
## 1           x  1  1   450
## 2           x  2  1     0
## 3           x  3  1   222
## 4           x  4  1     0
## 5           x  5  1     0
## 6           x  6  1   147
## 7           x  7  1     0
## 8           x  8  1   143
## 9           x  9  1     0
## 10          x 10  1     0
## 11          x 11  1   114
## 12          x 12  1     0
## 13          x 13  1   101
## 14          x 14  1     0
## 15          x 15  1     0
## 16          x 16  1     0
## 17          x 17  1     0
## 18          x 18  1     0
## 19          x 19  1     0
## 20          x 20  1    66
## 21          x 21  1    62
## 22          x 22  1     0
## 23          x 23  1     0
## 24          x 24  1     0
## 25          x 25  1    54
## 26          x 26  1     0
## 27          x 27  1    52
## 28          x 28  1     0
## 29          x 29  1    50
## 30          x 30  1    49
## 31          x 31  1    48
## 32          x 32  1     0
## 33          x 33  1    41
## 34          x 34  1    37
## 35          x 35  1     0
## 36          x 36  1     0
## 37          x 37  1    33
## 38          x 38  1     0
## 39          x 39  1    30
## 40          x 40  1     0
## 41          x 41  1    30
## 42          x 42  1     0
## 43          x 43  1    26
## 44          x 44  1     0
## 45          x 45  1     0
## 46          x 46  1     0
## 47          x 47  1     0
## 48          x 48  1     0
## 49          x 49  1     0
## 50          x 50  1     0
## 51          x  1  2     0
## 52          x  2  2     0
## 53          x  3  2     0
## 54          x  4  2     0
## 55          x  5  2     0
## 56          x  6  2     0
## 57          x  7  2     0
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get_solution(result, y[j])
##    variable  j value
## 1         y  1     1
## 2         y  2     0
## 3         y  3     0
## 4         y  4     0
## 5         y  5     1
## 6         y  6     0
## 7         y  7     0
## 8         y  8     0
## 9         y  9     0
## 10        y 10     0
## 11        y 11     0
## 12        y 12     0
## 13        y 13     0
## 14        y 14     0
## 15        y 15     0
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## 20        y 20     0
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## 22        y 22     0
## 23        y 23     0
## 24        y 24     0
## 25        y 25     0
## 26        y 26     0
## 27        y 27     0
## 28        y 28     0
## 29        y 29     0
## 30        y 30     0
## 31        y 31     0
## 32        y 32     0
## 33        y 33     0
## 34        y 34     0
## 35        y 35     0
## 36        y 36     0
## 37        y 37     0
## 38        y 38     0
## 39        y 39     0
## 40        y 40     0
## 41        y 41     0
## 42        y 42     0
## 43        y 43     0
## 44        y 44     0
## 45        y 45     0
## 46        y 46     0
## 47        y 47     0
## 48        y 48     0
## 49        y 49     0
## 50        y 50     0
#cities_10 <- read_csv("distances_top_10.csv")
solution <- as_tibble(get_solution(result, x[i,j]))
solution
## # A tibble: 2,500 x 4
##    variable     i     j value
##    <chr>    <int> <int> <dbl>
##  1 x            1     1   450
##  2 x            2     1     0
##  3 x            3     1   222
##  4 x            4     1     0
##  5 x            5     1     0
##  6 x            6     1   147
##  7 x            7     1     0
##  8 x            8     1   143
##  9 x            9     1     0
## 10 x           10     1     0
## # … with 2,490 more rows
library(dplyr)
# get hub solution
solution_hub <- as_tibble(get_solution(result, y[j]))
to.column <- as.vector(get_supply$to)
solution_hub <- solution_hub %>% 
  add_column(Hub = 0)
solution_hub$Hub <- to.column
solution_hub
## # A tibble: 50 x 4
##    variable     j value Hub                             
##    <chr>    <int> <dbl> <chr>                           
##  1 y            1     1 New York, New York              
##  2 y            2     0 Los Angeles, California         
##  3 y            3     0 Chicago, Illinois               
##  4 y            4     0 Dallas, Texas                   
##  5 y            5     1 Houston, Texas                  
##  6 y            6     0 Washington, District of Columbia
##  7 y            7     0 Miami, Florida                  
##  8 y            8     0 Philadelphia, Pennsylvania      
##  9 y            9     0 Atlanta, Georgia                
## 10 y           10     0 Phoenix, Arizona                
## # … with 40 more rows
# Adds after the second column
solution <- solution %>%
  add_column(FROM_city = 0) %>% 
  add_column(TO_city = 0) %>% 
  add_column(lon.to = 0) %>%
  add_column(lat.to = 0) %>%
  add_column(lon.from = 0) %>%
  add_column(lat.from = 0)

#m <- 1
for ( k in 1:length(city_data$lon.to)){
  solution$FROM_city[k] <- city_data$from[k]
  solution$lon.from[k] <- city_data$lon.from[k]
  solution$lat.from[k] <- city_data$lat.from[k]
  solution$TO_city[k] <- city_data$to[k]
  solution$lon.to[k] <- city_data$lon.to[k]
  solution$lat.to[k] <- city_data$lat.to[k]
  #m < m + 1

}
solution
## # A tibble: 2,500 x 10
##    variable     i     j value FROM_city  TO_city lon.to lat.to lon.from lat.from
##    <chr>    <int> <int> <dbl> <chr>      <chr>    <dbl>  <dbl>    <dbl>    <dbl>
##  1 x            1     1   450 New York,… New Yo…  -74.0   40.7    -74.0     40.7
##  2 x            2     1     0 Los Angel… New Yo…  -74.0   40.7   -118.      34.1
##  3 x            3     1   222 Chicago, … New Yo…  -74.0   40.7    -87.6     41.9
##  4 x            4     1     0 Dallas, T… New Yo…  -74.0   40.7    -96.8     32.8
##  5 x            5     1     0 Houston, … New Yo…  -74.0   40.7    -95.4     29.8
##  6 x            6     1   147 Washingto… New Yo…  -74.0   40.7    -77.0     38.9
##  7 x            7     1     0 Miami, Fl… New Yo…  -74.0   40.7    -80.2     25.8
##  8 x            8     1   143 Philadelp… New Yo…  -74.0   40.7    -75.2     40.0
##  9 x            9     1     0 Atlanta, … New Yo…  -74.0   40.7    -84.4     33.7
## 10 x           10     1     0 Phoenix, … New Yo…  -74.0   40.7   -112.      33.4
## # … with 2,490 more rows
# from.column <- c(cities_10$to[1:10])
# to.column <- c("Houston, Texas", "Washington, District of Columbia")
# m <- 1
# n <- 0
# for (k in 1:2){
#   for (l in 1:10){
#     solution$FROM_city[m] <- from.column[l]
#     solution$lon.from[m] <- cities_10$lon.to[l]
#     solution$lat.from[m] <- cities_10$lat.to[l]
#     solution$TO_city[m] <- to.column[k]
#     solution$lon.to[m] <- cities_10$lon.to[5 + n]
#     solution$lat.to[m] <- cities_10$lat.to[5 + n]
#     m <- m + 1
#   }
#   n <- n + 1
# }

### This works!!!
# no clean it up
solution <- solution %>% 
  filter(value > 0)



#### now map it ####
library(tidyverse)


# "us.cities" in maps package contains This database is of us cities of population
# greater than about 40,000. Also included are state capitals of any 
# population size.
# "state" database produces a map of the states of the United States
# mainland generated from US De- partment of the Census data
library(maps)

# Read in 10 city data with distances made in "Get Distances"
cities_10 <- read_csv("distances_top_10.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
# Get states for plotting state map
us_states <- as_tibble(map_data("state"))


ggplot(data = us_states, mapping = aes(x = long, y = lat,
                                       group = group)) +
  geom_polygon(fill= "white", color = "black") +
  geom_point(data = city_data, aes( x = lon.from, y = lat.from,
                                    size = from_population, color = "purple", alpha = 0.5),
             inherit.aes = FALSE) +
  geom_text(data = city_data, aes(x = lon.from, y = lat.from, label = from), inherit.aes = FALSE) +
  geom_segment(data = solution, aes(x = lon.from, y = lat.from, xend = lon.to,
                                    yend = lat.to), color = "blue", size = 0.3,
               arrow = arrow(), inherit.aes = FALSE)

Let’s 50 C, best 2 hubs, any hubs

# Choose more than two, any two

#### import data set ####
library(readr)
library(tidyr)
library(dplyr)
# Read in .csv file and create Tibble DF.
cities_raw <- read_csv("distances_my_top_50.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
# Turn into a dataframe
city_data <- as_tibble(cities_raw)
get_supply <- as_tibble(cities_raw)
# Add a number for each city 1 to 50
city_data <- city_data %>% 
  add_column(num.from = 0, .after = 4) %>% 
  add_column(num.to = 0, .after = 6)
  
# number from and to numbers
xx <- 1
for (ii in 1:50){
  for (jj in 1:50) {
    city_data$num.from[xx] <- ii
    city_data$num.to[xx] <- jj
    xx <- xx + 1
  }
}


# Choose number of cities to use
num_cities <- 50

#data <- as.data.frame(Network_Modeling)
# Get top six in each set of TO and FROM
# city_data <- city_data %>% 
#   group_by(num.from) %>%
#   slice_min(order_by = num.from, n = num_cities) %>%
#   group_by(num.to) %>%
#   slice_min(order_by = num.to, n = num_cities) %>%
#   arrange(num.from)

city_data <- city_data %>% 
  group_by(num.from) %>%
  slice_head(n = num_cities) %>% 
  group_by(num.to) %>% 
  slice_head(n = num_cities) %>% 
  group_by(num.from)
  

# redo number of cars from each city
# get supply
num_cars_month <- 4000
#library(dplyr)
get_supply <- get_supply %>% 
  slice_head(n = num_cities) %>% 
  #arrange(desc(Population)) %>% # sort Tibble by Population and descending
  #slice_head(n = 11) %>% # Get only the first n rows.
  mutate(to_pop_ratio = to_population / sum(to_population)) %>% # percent of Population
  mutate(to_num_cars = round(to_pop_ratio * num_cars_month,0)) # Calc number cars moving each month

# make into a cost matrix
cost <- city_data$cost
cost_6_city <- matrix(cost, nrow = num_cities, byrow = FALSE)


library(ompr)
library(magrittr)
library(ROI)
library(ROI.plugin.glpk)
library(ompr)
library(ompr.roi)
# Shipping Cost
# cost <- c(705.04,690.03,593.44,332.01,100.00,662.94,617.15,689.96,522.36,614.42,
#           326.04,874.85,496.92,646.68,662.94,100.00,586.57,277.47,478.96,819.49)
# cost_m <- matrix(cost, nrow = 10, byrow = FALSE)
# cost_m
# Supply to move from each cities
#supply <- as.vector(city_data$`Number of cars Shipped From`[1:6])
# the above wasn't resized for 6 cities
supply <- as.vector(get_supply$to_num_cars)

# model <- MIPModel()  %>% 
#   # Number of cars shiped from Xi to Xj
#   add_variable(x[i,j], i = 1:6, j = 1:6, type = "integer", lb = 0) %>% 
#   # Choose Houston (Y1) or Washington (Y2)
#   add_variable(y[j], j = 1:6, type = "binary") %>% 
#   #add_variable(y[j], j = 1:2, type = "integer", lb = 0, ub = 1)
#   # minimize shipping cost
#   set_objective(sum_expr(cost_6_city[i,j] * x[i,j], i = 1:6, j = 1:6), "min") %>% 
#   # must use supply from each city
#   
#   ### fix this with J's, not 1 and 2
#   #add_constraint(x[i, 1] + x[i, 2] >= supply[i], i = 1:10) #%>%
#   # FIXED! works with j's
#   add_constraint(sum_expr(x[i, j], j = 1:6) >= supply[i], i = 1:6) %>% 
#   # add this to keep Houston
#   add_constraint(y[5] == 1) %>% 
#   add_constraint(sum_expr(y[j], j = 1:6) == 2) %>% 
#   # add linking variables
#   # 1500 because the new limit should be 1224
#   add_constraint(x[i,j] <= 1500*y[j], i = 1:6, j = 1:6)
# 
# 
# #result <- ROI_solve(model, solver = "glpk")
# result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
# result
# get_solution(result, x[i,j])
# get_solution(result, y[j])


num_hubs <- 2

model <- MIPModel()  %>% 
  # Number of cars shiped from Xi to Xj
  add_variable(x[i,j], i = 1:length(supply), j = 1:length(supply), type = "integer", lb = 0) %>% 
  # Choose Houston (Y1) or Washington (Y2)
  add_variable(y[j], j = 1:length(supply), type = "binary") %>% 
  #add_variable(y[j], j = 1:2, type = "integer", lb = 0, ub = 1)
  # minimize shipping cost
  set_objective(sum_expr(cost_6_city[i,j] * x[i,j], i = 1:length(supply), j = 1:length(supply)), "min") %>% 
  # must use supply from each city
  
  ### fix this with J's, not 1 and 2
  #add_constraint(x[i, 1] + x[i, 2] >= supply[i], i = 1:10) #%>%
  # FIXED! works with j's
  add_constraint(sum_expr(x[i, j], j = 1:length(supply)) >= supply[i], i = 1:length(supply)) %>% 
  # add this to keep Houston
  #add_constraint(y[5] == 1) %>% 
  add_constraint(sum_expr(y[j], j = 1:length(supply)) == num_hubs) %>% 
  # add linking variables
  # 1500 because the new limit should be 1224
  add_constraint(x[i,j] <= max(supply)*y[j], i = 1:length(supply), j = 1:length(supply))
## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.

## Warning: There are variables in your environment that interfere with your
## defined model variables: x. This can lead to unexpected behaviour.
#result <- ROI_solve(model, solver = "glpk")
result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))
## <SOLVER MSG>  ----
## GLPK Simplex Optimizer, v4.65
## 2551 rows, 2550 columns, 7550 non-zeros
##       0: obj =   0.000000000e+00 inf =   4.004e+03 (51)
##      52: obj =   2.229404654e+06 inf =   0.000e+00 (0)
## *   446: obj =   1.217775484e+06 inf =   0.000e+00 (0) 1
## OPTIMAL LP SOLUTION FOUND
## GLPK Integer Optimizer, v4.65
## 2551 rows, 2550 columns, 7550 non-zeros
## 2550 integer variables, 50 of which are binary
## Integer optimization begins...
## Long-step dual simplex will be used
## +   446: mip =     not found yet >=              -inf        (1; 0)
## +  1217: >>>>>   1.779829999e+06 >=   1.250542718e+06  29.7% (50; 0)
## + 11621: >>>>>   1.744114448e+06 >=   1.293008140e+06  25.9% (397; 18)
## + 15446: >>>>>   1.735643485e+06 >=   1.339215786e+06  22.8% (487; 64)
## + 20914: >>>>>   1.693903928e+06 >=   1.428621180e+06  15.7% (642; 102)
## + 58391: mip =   1.693903928e+06 >=     tree is empty   0.0% (0; 1699)
## INTEGER OPTIMAL SOLUTION FOUND
## <!SOLVER MSG> ----
result
## Status: optimal
## Objective value: 1693904
get_solution(result, x[i,j])
##      variable  i  j value
## 1           x  1  1     0
## 2           x  2  1     0
## 3           x  3  1     0
## 4           x  4  1     0
## 5           x  5  1     0
## 6           x  6  1     0
## 7           x  7  1     0
## 8           x  8  1     0
## 9           x  9  1     0
## 10          x 10  1     0
## 11          x 11  1     0
## 12          x 12  1     0
## 13          x 13  1     0
## 14          x 14  1     0
## 15          x 15  1     0
## 16          x 16  1     0
## 17          x 17  1     0
## 18          x 18  1     0
## 19          x 19  1     0
## 20          x 20  1     0
## 21          x 21  1     0
## 22          x 22  1     0
## 23          x 23  1     0
## 24          x 24  1     0
## 25          x 25  1     0
## 26          x 26  1     0
## 27          x 27  1     0
## 28          x 28  1     0
## 29          x 29  1     0
## 30          x 30  1     0
## 31          x 31  1     0
## 32          x 32  1     0
## 33          x 33  1     0
## 34          x 34  1     0
## 35          x 35  1     0
## 36          x 36  1     0
## 37          x 37  1     0
## 38          x 38  1     0
## 39          x 39  1     0
## 40          x 40  1     0
## 41          x 41  1     0
## 42          x 42  1     0
## 43          x 43  1     0
## 44          x 44  1     0
## 45          x 45  1     0
## 46          x 46  1     0
## 47          x 47  1     0
## 48          x 48  1     0
## 49          x 49  1     0
## 50          x 50  1     0
## 51          x  1  2     0
## 52          x  2  2   310
## 53          x  3  2     0
## 54          x  4  2     0
## 55          x  5  2     0
## 56          x  6  2     0
## 57          x  7  2     0
## 58          x  8  2     0
## 59          x  9  2     0
## 60          x 10  2   116
## 61          x 11  2     0
## 62          x 12  2   111
## 63          x 13  2     0
## 64          x 14  2    93
## 65          x 15  2     0
## 66          x 16  2    78
## 67          x 17  2     0
## 68          x 18  2    69
## 69          x 19  2     0
## 70          x 20  2     0
## 71          x 21  2     0
## 72          x 22  2     0
## 73          x 23  2    60
## 74          x 24  2    58
## 75          x 25  2     0
## 76          x 26  2    53
## 77          x 27  2     0
## 78          x 28  2     0
## 79          x 29  2     0
## 80          x 30  2     0
## 81          x 31  2     0
## 82          x 32  2     0
## 83          x 33  2     0
## 84          x 34  2     0
## 85          x 35  2     0
## 86          x 36  2    33
## 87          x 37  2     0
## 88          x 38  2     0
## 89          x 39  2     0
## 90          x 40  2     0
## 91          x 41  2     0
## 92          x 42  2    29
## 93          x 43  2     0
## 94          x 44  2     0
## 95          x 45  2     0
## 96          x 46  2    22
## 97          x 47  2    18
## 98          x 48  2     0
## 99          x 49  2    13
## 100         x 50  2     0
## 101         x  1  3     0
## 102         x  2  3     0
## 103         x  3  3     0
## 104         x  4  3     0
## 105         x  5  3     0
## 106         x  6  3     0
## 107         x  7  3     0
## 108         x  8  3     0
## 109         x  9  3     0
## 110         x 10  3     0
## 111         x 11  3     0
## 112         x 12  3     0
## 113         x 13  3     0
## 114         x 14  3     0
## 115         x 15  3     0
## 116         x 16  3     0
## 117         x 17  3     0
## 118         x 18  3     0
## 119         x 19  3     0
## 120         x 20  3     0
## 121         x 21  3     0
## 122         x 22  3     0
## 123         x 23  3     0
## 124         x 24  3     0
## 125         x 25  3     0
## 126         x 26  3     0
## 127         x 27  3     0
## 128         x 28  3     0
## 129         x 29  3     0
## 130         x 30  3     0
## 131         x 31  3     0
## 132         x 32  3     0
## 133         x 33  3     0
## 134         x 34  3     0
## 135         x 35  3     0
## 136         x 36  3     0
## 137         x 37  3     0
## 138         x 38  3     0
## 139         x 39  3     0
## 140         x 40  3     0
## 141         x 41  3     0
## 142         x 42  3     0
## 143         x 43  3     0
## 144         x 44  3     0
## 145         x 45  3     0
## 146         x 46  3     0
## 147         x 47  3     0
## 148         x 48  3     0
## 149         x 49  3     0
## 150         x 50  3     0
## 151         x  1  4     0
## 152         x  2  4     0
## 153         x  3  4     0
## 154         x  4  4     0
## 155         x  5  4     0
## 156         x  6  4     0
## 157         x  7  4     0
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## 159         x  9  4     0
## 160         x 10  4     0
## 161         x 11  4     0
## 162         x 12  4     0
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## 164         x 14  4     0
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## 167         x 17  4     0
## 168         x 18  4     0
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## 172         x 22  4     0
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## 174         x 24  4     0
## 175         x 25  4     0
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## 182         x 32  4     0
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## 185         x 35  4     0
## 186         x 36  4     0
## 187         x 37  4     0
## 188         x 38  4     0
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## 190         x 40  4     0
## 191         x 41  4     0
## 192         x 42  4     0
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## 194         x 44  4     0
## 195         x 45  4     0
## 196         x 46  4     0
## 197         x 47  4     0
## 198         x 48  4     0
## 199         x 49  4     0
## 200         x 50  4     0
## 201         x  1  5     0
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## 205         x  5  5     0
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## 224         x 24  5     0
## 225         x 25  5     0
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## 230         x 30  5     0
## 231         x 31  5     0
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## 251         x  1  6   450
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## 255         x  5  6   165
## 256         x  6  6   147
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## 260         x 10  6     0
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## 285         x 35  6    37
## 286         x 36  6     0
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## 291         x 41  6    30
## 292         x 42  6     0
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## 295         x 45  6    22
## 296         x 46  6     0
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## 299         x 49  6     0
## 300         x 50  6    10
## 301         x  1  7     0
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## 305         x  5  7     0
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## 325         x 25  7     0
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get_solution(result, y[j])
##    variable  j value
## 1         y  1     0
## 2         y  2     1
## 3         y  3     0
## 4         y  4     0
## 5         y  5     0
## 6         y  6     1
## 7         y  7     0
## 8         y  8     0
## 9         y  9     0
## 10        y 10     0
## 11        y 11     0
## 12        y 12     0
## 13        y 13     0
## 14        y 14     0
## 15        y 15     0
## 16        y 16     0
## 17        y 17     0
## 18        y 18     0
## 19        y 19     0
## 20        y 20     0
## 21        y 21     0
## 22        y 22     0
## 23        y 23     0
## 24        y 24     0
## 25        y 25     0
## 26        y 26     0
## 27        y 27     0
## 28        y 28     0
## 29        y 29     0
## 30        y 30     0
## 31        y 31     0
## 32        y 32     0
## 33        y 33     0
## 34        y 34     0
## 35        y 35     0
## 36        y 36     0
## 37        y 37     0
## 38        y 38     0
## 39        y 39     0
## 40        y 40     0
## 41        y 41     0
## 42        y 42     0
## 43        y 43     0
## 44        y 44     0
## 45        y 45     0
## 46        y 46     0
## 47        y 47     0
## 48        y 48     0
## 49        y 49     0
## 50        y 50     0
#cities_10 <- read_csv("distances_top_10.csv")
solution <- as_tibble(get_solution(result, x[i,j]))
solution
## # A tibble: 2,500 x 4
##    variable     i     j value
##    <chr>    <int> <int> <dbl>
##  1 x            1     1     0
##  2 x            2     1     0
##  3 x            3     1     0
##  4 x            4     1     0
##  5 x            5     1     0
##  6 x            6     1     0
##  7 x            7     1     0
##  8 x            8     1     0
##  9 x            9     1     0
## 10 x           10     1     0
## # … with 2,490 more rows
library(dplyr)
# get hub solution
solution_hub <- as_tibble(get_solution(result, y[j]))
to.column <- as.vector(get_supply$to)
solution_hub <- solution_hub %>% 
  add_column(Hub = 0)
solution_hub$Hub <- to.column
solution_hub
## # A tibble: 50 x 4
##    variable     j value Hub                             
##    <chr>    <int> <dbl> <chr>                           
##  1 y            1     0 New York, New York              
##  2 y            2     1 Los Angeles, California         
##  3 y            3     0 Chicago, Illinois               
##  4 y            4     0 Dallas, Texas                   
##  5 y            5     0 Houston, Texas                  
##  6 y            6     1 Washington, District of Columbia
##  7 y            7     0 Miami, Florida                  
##  8 y            8     0 Philadelphia, Pennsylvania      
##  9 y            9     0 Atlanta, Georgia                
## 10 y           10     0 Phoenix, Arizona                
## # … with 40 more rows
# Adds after the second column
solution <- solution %>%
  add_column(FROM_city = 0) %>% 
  add_column(TO_city = 0) %>% 
  add_column(lon.to = 0) %>%
  add_column(lat.to = 0) %>%
  add_column(lon.from = 0) %>%
  add_column(lat.from = 0)

#m <- 1
for ( k in 1:length(city_data$lon.to)){
  solution$FROM_city[k] <- city_data$from[k]
  solution$lon.from[k] <- city_data$lon.from[k]
  solution$lat.from[k] <- city_data$lat.from[k]
  solution$TO_city[k] <- city_data$to[k]
  solution$lon.to[k] <- city_data$lon.to[k]
  solution$lat.to[k] <- city_data$lat.to[k]
  #m < m + 1

}
solution
## # A tibble: 2,500 x 10
##    variable     i     j value FROM_city  TO_city lon.to lat.to lon.from lat.from
##    <chr>    <int> <int> <dbl> <chr>      <chr>    <dbl>  <dbl>    <dbl>    <dbl>
##  1 x            1     1     0 New York,… New Yo…  -74.0   40.7    -74.0     40.7
##  2 x            2     1     0 Los Angel… New Yo…  -74.0   40.7   -118.      34.1
##  3 x            3     1     0 Chicago, … New Yo…  -74.0   40.7    -87.6     41.9
##  4 x            4     1     0 Dallas, T… New Yo…  -74.0   40.7    -96.8     32.8
##  5 x            5     1     0 Houston, … New Yo…  -74.0   40.7    -95.4     29.8
##  6 x            6     1     0 Washingto… New Yo…  -74.0   40.7    -77.0     38.9
##  7 x            7     1     0 Miami, Fl… New Yo…  -74.0   40.7    -80.2     25.8
##  8 x            8     1     0 Philadelp… New Yo…  -74.0   40.7    -75.2     40.0
##  9 x            9     1     0 Atlanta, … New Yo…  -74.0   40.7    -84.4     33.7
## 10 x           10     1     0 Phoenix, … New Yo…  -74.0   40.7   -112.      33.4
## # … with 2,490 more rows
# from.column <- c(cities_10$to[1:10])
# to.column <- c("Houston, Texas", "Washington, District of Columbia")
# m <- 1
# n <- 0
# for (k in 1:2){
#   for (l in 1:10){
#     solution$FROM_city[m] <- from.column[l]
#     solution$lon.from[m] <- cities_10$lon.to[l]
#     solution$lat.from[m] <- cities_10$lat.to[l]
#     solution$TO_city[m] <- to.column[k]
#     solution$lon.to[m] <- cities_10$lon.to[5 + n]
#     solution$lat.to[m] <- cities_10$lat.to[5 + n]
#     m <- m + 1
#   }
#   n <- n + 1
# }

### This works!!!
# no clean it up
solution <- solution %>% 
  filter(value > 0)



#### now map it ####
library(tidyverse)


# "us.cities" in maps package contains This database is of us cities of population
# greater than about 40,000. Also included are state capitals of any 
# population size.
# "state" database produces a map of the states of the United States
# mainland generated from US De- partment of the Census data
library(maps)

# Read in 10 city data with distances made in "Get Distances"
cities_10 <- read_csv("distances_top_10.csv")
## 
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
##   lon.to = col_double(),
##   lat.to = col_double(),
##   lon.from = col_double(),
##   lat.from = col_double(),
##   from = col_character(),
##   to = col_character(),
##   distance = col_double(),
##   from_population = col_double(),
##   from_pop_ratio = col_double(),
##   from_num_cars = col_double(),
##   to_population = col_double(),
##   to_pop_ratio = col_double(),
##   to_num_cars = col_double(),
##   cost = col_double()
## )
# Get states for plotting state map
us_states <- as_tibble(map_data("state"))


ggplot(data = us_states, mapping = aes(x = long, y = lat,
                                       group = group)) +
  geom_polygon(fill= "white", color = "black") +
  geom_point(data = city_data, aes( x = lon.from, y = lat.from,
                                    size = from_population, color = "purple", alpha = 0.5),
             inherit.aes = FALSE) +
  geom_text(data = city_data, aes(x = lon.from, y = lat.from, label = from), inherit.aes = FALSE) +
  geom_segment(data = solution, aes(x = lon.from, y = lat.from, xend = lon.to,
                                    yend = lat.to), color = "blue", size = 0.3,
               arrow = arrow(), inherit.aes = FALSE)

You started with Houston and want to keep it.

now sensitivity analysis

what if we change cost to ship, will that change cities hub?

what if we add capital cost to build a new hub and it matches city population, we, of course , could do more in depth analysis for real estate and include that

Step 2: Plot data

Step 3:

Step 4:

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